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This paper explores the likelihood and Bayesian estimation of the stress–strength reliability parameter (R) based on a lower record ranked set sampling scheme from the generalized Rayleigh distribution. Maximum likelihood and Bayesian estimators as well as confidence intervals of R are derived and their properties are studied. Furthermore, two parametric bootstrap confidence intervals are introduced in the paper. A comparative simulation study is conducted to assess the effectiveness of these four confidence interval methodologies in estimating R. The application of the methods is demonstrated using real data on fiber strength to showcase their practicability and relevance in the industry. [ABSTRACT FROM AUTHOR]

The usage of psychological networks that conceptualize behavior as a complex interplay of psychological and other components has gained increasing popularity in various research fields. While prior publications have tackled the topics of estimating and interpreting such networks, little work has been conducted to check how accurate (i.e., prone to sampling variation) networks are estimated, and how stable (i.e., interpretation remains similar with less observations) inferences from the network structure (such as centrality indices) are. In this tutorial paper, we aim to introduce the reader to this field and tackle the problem of accuracy under sampling variation. We first introduce the current state-of-the-art of network estimation. Second, we provide a rationale why researchers should investigate the accuracy of psychological networks. Third, we describe how bootstrap routines can be used to (A) assess the accuracy of estimated network connections, (B) investigate the stability of centrality indices, and (C) test whether network connections and centrality estimates for different variables differ from each other. We introduce two novel statistical methods: for (B) the correlation stability coefficient, and for (C) the bootstrapped difference test for edge-weights and centrality indices. We conducted and present simulation studies to assess the performance of both methods. Finally, we developed the free R-package bootnet that allows for estimating psychological networks in a generalized framework in addition to the proposed bootstrap methods. We showcase bootnet in a tutorial, accompanied by R syntax, in which we analyze a dataset of 359 women with posttraumatic stress disorder available online. [ABSTRACT FROM AUTHOR]

This paper proposes a bootstrap testing approach based on an approximate maximum likelihood method to discern whether a diffusion process is linear or whether there are threshold effects in the drift, the diffusion term or in both. It complements an alternative method based on the least-squares estimator which focuses on threshold effects in the drift. Monte Carlo simulations illustrate that the proposed testing approach is able to detect the source of the non-linearity. Two empirical applications show the importance of modeling threshold effects in the diffusion instead of the drift. [ABSTRACT FROM AUTHOR]

In this paper, we present some results to make inference about the parameters of lower truncated proportional hazard rate models with the same baseline distributions based on three independent generalized order statistics samples. Then, especially by considering the results of the diagnostic tests for the non-diseased, early-diseased stage and fully diseased populations, we make inference about sensitivity to the early disease stage parameter. The maximum likelihood estimator, a generalized pivotal estimator and some Bayes estimators are obtained for different structures of prior distributions. The percentile bootstrap confidence interval, a generalized pivotal confidence interval and some Bayesian credible intervals are also presented. A Monte Carlo simulation study is used to evaluate the performances of the obtained point estimators and confidence/credible intervals and two competitors. We use two real datasets to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

Remote sensing products are typically assessed using a single accuracy estimate for the entire map, despite significant variations in accuracy across different map areas or classes. Estimating per-pixel uncertainty is a major challenge for enhancing the usability and potential of remote sensing products. This paper introduces the dataDriven open access tool, a novel statistical design-based approach that specifically addresses this issue by estimating per-pixel uncertainty through a bootstrap resampling procedure. Leveraging Sentinel-2 remote sensing data as auxiliary information, the capabilities of the Google Earth Engine cloud computing platform, and the R programming language, dataDriven can be applied in any world region and variables of interest. In this study, the dataDriven tool was tested in the Rincine forest estate study area—eastern Tuscany, Italy—focusing on volume density as the variable of interest. The average volume density was 0.042, corresponding to 420 m3 per hectare. The estimated pixel errors ranged between 93 m3 and 979 m3 per hectare and were 285 m3 per hectare on average. The ability to produce error estimates for each pixel in the map is a novel aspect in the context of the current advances in remote sensing and forest monitoring and assessment. It constitutes a significant support in forest management applications and also a powerful communication tool since it informs users about areas where map estimates are unreliable, at the same time highlighting the areas where the information provided via the map is more trustworthy. In light of this, the dataDriven tool aims to support researchers and practitioners in the spatially exhaustive use of remote sensing-derived products and map validation. [ABSTRACT FROM AUTHOR]

Optimizing structural designs is crucial today, with additive manufacturing, particularly selective laser melting, gaining prominence. Thorough mechanical characterization of new materials remains vital. This paper investigates fatigue crack growth behavior in SLM 316L specimens under cyclic loading conditions. The study addresses result uncertainties by using CT specimens aligned along three building directions per ASTM E647 standards and a constant loading ratio (R = 0.1), necessitating mean value and confidence interval predictions. Departing from linear prediction models, innovative Bootstrap Polynomial and Power Regression Models and Bayesian Nonlinear Regression Model updated posterior distribution by Markov Chain Monte Carlo are employed. These approaches leverage bootstrapping to construct confidence intervals, offering robustness and flexibility in handling non‐normal data behavior and limited sample sizes. They provide tailored fits to data curvature, revealing limitations of linear prediction models in capturing observed nonlinear behavior, enhancing reliability in additive manufacturing applications, and advancing material science and engineering. [ABSTRACT FROM AUTHOR]

The high-speed railway subgrade compaction quality is controlled by the compaction degree (K), with the maximum dry density (ρdmax) serving as a crucial indicator for its calculation. The current mechanisms and methods for determining the ρdmax still suffer from uncertainties, inefficiencies, and lack of intelligence. These deficiencies can lead to insufficient assessments for the high-speed railway subgrade compaction quality, further impacting the operational safety of high-speed railways. In this paper, a novel method for full-section assessment of high-speed railway subgrade compaction quality based on ML-interval prediction theory is proposed. Firstly, based on indoor vibration compaction tests, a method for determining the ρdmax based on the dynamic stiffness Krb turning point is proposed. Secondly, the Pso-OptimalML-Adaboost (POA) model for predicting ρdmax is determined based on three typical machine learning (ML) algorithms, which are back propagation neural network (BPNN), support vector regression (SVR), and random forest (RF). Thirdly, the interval prediction theory is introduced to quantify the uncertainty in ρdmax prediction. Finally, based on the Bootstrap-POA-ANN interval prediction model and spatial interpolation algorithms, the interval distribution of ρdmax across the full-section can be determined, and a model for full-section assessment of compaction quality is developed based on the compaction standard (95%). Moreover, the proposed method is applied to determine the optimal compaction thicknesses (H0), within the station subgrade test section in the southwest region. The results indicate that: (1) The PSO-BPNN-AdaBoost model performs better in the accuracy and error metrics, which is selected as the POA model for predicting ρdmax. (2) The Bootstrap-POA-ANN interval prediction model for ρdmax can construct clear and reliable prediction intervals. (3) The model for full-section assessment of compaction quality can provide the full-section distribution interval for K. Comparing the H0 of 50~60 cm and 60~70 cm, the compaction quality is better with the H0 of 40~50 cm. The research findings can provide effective techniques for assessing the compaction quality of high-speed railway subgrades. [ABSTRACT FROM AUTHOR]

Estimation of reliability and stress–strength parameters is important in the manufacturing industry. In this paper, we develop shrinkage-type estimators for the reliability and stress–strength parameters based on progressively censored data from a rich class of distributions. These new estimators improve the performance of the commonly used Maximum Likelihood Estimators (MLEs) by reducing their mean squared errors. We provide analytical asymptotic and bootstrap confidence intervals for the targeted parameters. Through a detailed simulation study, we demonstrate that the new estimators have better performance than the MLEs. Finally, we illustrate the application of the new methods to two industrial data sets, showcasing their practical relevance and effectiveness. [ABSTRACT FROM AUTHOR]

We carry on a long term analysis for Bitcoin price, which is currently among the most renowned crypto assets available on markets other than Forex. In the last decade Bitcoin has been under spotlights among traders all world wide, both because of its nature of pseudo–currency and for the high volatility its price has frequently experienced. Considering that Bitcoin price has earned over five orders of magnitude since 2009, the interest of investors has been increasingly motivated by the necessity of accurately predicting its value, not to mention that a comparative analysis with other assets as silver and gold has been under investigation, too. This paper reports two approaches for a long term Bitcoin price prediction. The first one follows more standard paradigms from regression and least squares frameworks. Our main contribution in this regard fosters conclusions which are able to justify the cyclic performance of Bitcoin price, in terms of its Stock–to–Flow. Our second approach is definitely novel in the literature, and indicates guidelines for long term forecasts of Bitcoin price based on Machine Learning (ML) methods, with a specific reference to Support Vector Machines (SVMs). Both these approaches are inherently data–driven, and the second one does not require any of the assumptions typically needed by solvers for classic regression problems. [ABSTRACT FROM AUTHOR]

Trajectory planning plays a crucial role in achieving unmanned excavator operations. The quality of trajectory planning results heavily relies on the level of rules extracted from objects such as scenes and optimization objectives, using traditional theoretical methods. To address this issue, this study focuses on professional operators and employs machine learning methods for job trajectory planning, thereby obtaining planned trajectories which exhibit excellent characteristics similar to those of professional operators. Under typical working conditions, data collection and analysis are conducted on the job trajectories of professional operators, with key points being extracted. Machine learning is then utilized to train models under different parameters in order to obtain the optimal model. To ensure sufficient samples for machine learning training, the bootstrap method is employed to adequately expand the sample size. Compared with the traditional spline curve method, the trajectories generated by machine learning models reduce the maximum speeds of excavator boom arm, dipper stick, bucket, and swing joint by 8.64 deg/s, 10.24 deg/s, 18.33 deg/s, and 1.6 deg/s, respectively; moreover, the error does not exceed 2.99 deg when compared with curves drawn by professional operators; and, finally, the trajectories generated by this model are continuously differentiable without position or velocity discontinuities, and their overall performance surpasses that of those generated by the traditional spline curve method. This paper proposes a trajectory generation method that combines excellent operators with machine learning and establishes a machine learning-based trajectory-planning model that eliminates the need for manually establishing complex rules. It is applicable to motion path planning in various working conditions of unmanned excavators. [ABSTRACT FROM AUTHOR]

In quality engineering, process capability indices play a crucial role in assessing the capability of a given process. Among the widely recognized indices are Cp, Cpk, Cpm, and Cpmk, all of which presuppose the normality of the product lifetime. However, Maiti et al. (2010) proposed a more versatile process capability index, denoted as Cpyk, which does not rely on distributional assumptions. The study is currently investigating statistical inferences for the Cpyk index within the context of progressively type-II censored samples, marking the first exploration of this aspect in the research. This paper investigates maximum likelihood and Bayesian inference for the Cpyk when the underlying distribution follows the inverse Rayleigh distribution. Additionally, the study explores Bayesian credible intervals and the highest posterior density intervals using the Markov Chain Monte Carlo procedure. Various types of bootstrap confidence intervals are also taken into consideration. To assess the performance of these intervals, a Monte Carlo simulation is executed, comparing their coverage probabilities and mean lengths. The paper concludes with an illustrative example utilizing real data, providing a practical application of the discussed methodologies. [ABSTRACT FROM AUTHOR]

Multicollinearity among independent variables is one of the most common problems in regression models. The aftereffects of this problem, such as ill-conditioning, instability of estimators, and inflating mean squared error of ordinary least squares estimator (OLS), in the multivariate linear regression model (MLRM) are the same that of linear regression models. To combat multicollinearity, several approaches have been presented in the literature. Liu estimator (LE), as a well known estimator in this connection, has been used in linear, generalized linear, and nonlinear regression models by researchers in recent years. In this paper, for the first time, LE and jackknifed Liu estimator (JLE) are investigated in MLRM. To improve estimators in the sense of mean squared error, two known resampling methods, i.e., jackknife and bootstrap, are used. Finally, OLS, LE, and JLE are compared by a simulation study and also using a real data set, by resampling methods in MLRM. [ABSTRACT FROM AUTHOR]

The Semi-variable Coefficient Spatial Lag Model (SVC-SLM) not only addresses the "dimension disaster" associated with the Varying Coefficient Spatial Lag Model(VC-SLM), but also overcomes the non-linear problem of the variable coefficient, and fully explores the hidden information of the model. In this paper, INLA is firstly used to estimate the parameters of (SVC-SLM) by using B-spline to deal with the non-parametric terms, and the comparative experimental results show that the INLA algorithm is much better than MCMCINLA in terms of both time efficiency and estimation accuracy. For the problem of identifying the constant coefficient terms in the SVC-SLM, the bootstrap test is given based on the residuals. Taking the PM2.5 data of 31 provinces in mainland China from 2015 to 2020 as an empirical example, parametric, non-parametric, and semi-parametric perspectives establish three models of Spatial Lag Model (SLM), VC-SLM, SVC-SLM, which explore the relationship between the covariate factors and the level of urbanization as well as their impacts on the concentration of PM2.5 in the context of increasing urbanization; among the three models, the SVC-SLM has the smallest values of DIC and WAIC, indicating that the SVC-SLM is optimal. [ABSTRACT FROM AUTHOR]

We consider an exchangeably weighted bootstrap for function-valued estimators defined as a zero point of a function-valued random criterion function. A large number of bootstrap resampling schemes emerge as special cases of our settings. The main ingredient is the use of a differential identity that applies when the random criterion function is linear in terms of the empirical measure. Our results are general and do not require linearity of the statistical model in terms of the unknown parameter. We also consider the semiparametric models extending Zhan's work to a more delicate framework. The theoretical results established in this paper are (or will be) key tools for further developments in the parametric and semiparametric models. [ABSTRACT FROM AUTHOR]

The early history of string theory is marked by a shift from strong interaction physics to quantum gravity. The first string models and associated theoretical framework were formulated in the late 1960s and early 1970s in the context of the S -matrix program for the strong interactions. In the mid-1970s, the models were reinterpreted as a potential theory unifying the four fundamental forces. This paper provides a historical analysis of how string theory was developed out of S -matrix physics, aiming to clarify how modern string theory, as a theory detached from experimental data, grew out of an S -matrix program that was strongly dependent upon observable quantities. Surprisingly, the theoretical practice of physicists already turned away from experiment before string theory was recast as a potential unified quantum gravity theory. With the formulation of dual resonance models (the "hadronic string theory"), physicists were able to determine almost all of the models' parameters on the basis of theoretical reasoning. It was this commitment to "non-arbitrariness", i.e., a lack of free parameters in the theory, that initially drove string theorists away from experimental input, and not the practical inaccessibility of experimental data in the context of quantum gravity physics. This is an important observation when assessing the role of experimental data in string theory. [ABSTRACT FROM AUTHOR]

This paper considers inference on the partial area under the receiver operating characteristic curve based on two independent progressively Type-II censored samples from the populations that are belonging to the lower truncated proportional hazard rate models with the same baseline distributions. The maximum likelihood estimator, a generalized pivotal estimator and some Bayes estimators are obtained for three structures of prior distributions. The percentile bootstrap confidence interval, a generalized pivotal confidence interval and some Bayesian credible intervals are also presented. A Monte-Carlo simulation study is used to evaluate the performances of the obtained point estimators and confidence and credible intervals. Finally, a real data set is applied for illustrative purposes. [ABSTRACT FROM AUTHOR]

Subsampling has seen a resurgence in the big data era where the standard, full-resample size bootstrap can be infeasible to compute. Nevertheless, even choosing a single random subsample of size b can be computationally challenging with both b and the sample size n being very large. This paper shows how a set of appropriately chosen, nonrandom subsamples can be used to conduct effective, and computationally feasible, subsampling distribution estimation. Furthermore, the same set of subsamples can be used to yield a procedure for subsampling aggregation, also known as subagging, that is scalable with big data. Interestingly, the scalable subagging estimator can be tuned to have the same, or better, rate of convergence than that of θ ^ n ⁠. Statistical inference could then be based on the scalable subagging estimator instead of the original θ ^ n ⁠. [ABSTRACT FROM AUTHOR]

A nonparametric procedure to estimate the conditional probability that a nonstationary geostatistical process exceeds a certain threshold value is proposed. The method consists of a bootstrap algorithm that combines conditional simulation techniques with nonparametric estimations of the trend and the variability. The nonparametric local linear estimator, considering a bandwidth matrix selected by a method that takes the spatial dependence into account, is used to estimate the trend. The variability is modeled estimating the conditional variance and the variogram from corrected residuals to avoid the biasses. The proposed method allows to obtain estimates of the conditional exceedance risk in non-observed spatial locations. The performance of the approach is analyzed by simulation and illustrated with the application to a real data set of precipitations in the USA.Supplementary materials accompanying this paper appear on-line. [ABSTRACT FROM AUTHOR]

The inverse probability of treatment weighting (IPTW) approach is commonly used in propensity score analysis to infer causal effects in regression models. Due to oversized IPTW weights and errors associated with propensity score estimation, the IPTW approach can underestimate the standard error of causal effect. To remediate this, bootstrap standard errors have been recommended to replace the IPTW standard error, but the ordinary bootstrap (OB) procedure might still result in underestimation of the standard error because of its inefficient resampling scheme and untreated oversized weights. In this paper, we develop a generalized bootstrap (GB) procedure for estimating the standard error and confidence intervals of the IPTW approach. Compared with the OB procedure and other three procedures in comparison, the GB procedure has the highest precision and yields conservative standard error estimates. As a result, the GB procedure produces short confidence intervals with highest coverage rates. We demonstrate the effectiveness of the GB procedure via two simulation studies and a dataset from the National Educational Longitudinal Study-1988 (NELS-88). [ABSTRACT FROM AUTHOR]

Tolerance intervals in regression allow the user to quantify, with a specified degree of confidence, bounds for a specified proportion of the sampled population when conditioned on a set of covariate values. While methods are available for tolerance intervals in fully-parametric regression settings, the construction of tolerance intervals for nonparametric regression models has been treated in a limited capacity. This paper fills this gap and develops likelihood-based approaches for the construction of pointwise one-sided and two-sided tolerance intervals for nonparametric regression models. A numerical approach is also presented for constructing simultaneous tolerance intervals. An appealing facet of this work is that the resulting methodology is consistent with what is done for fully-parametric regression tolerance intervals. Extensive coverage studies are presented, which demonstrate very good performance of the proposed methods. The proposed tolerance intervals are calculated and interpreted for analyses involving a fertility dataset and a triceps measurement dataset. [ABSTRACT FROM AUTHOR]

Numerous testing procedures for directional data have been proposed over the years and a natural question that springs is which to use and when. The aim of this paper is to answer this question, via a large scale Monte Carlo simulation study that covers circular and spherical data for the two mean directions problem. The results evidently signify that tests assuming equal concentration parameters should be avoided as they tend to inflate the test size, while the heterogeneous test that does not make this assumption is to be preferred, but unfortunately only with large sample sizes. Permutation calibration does not improve the performance of any testing procedure, whereas bootstrap does. Specifically, bootstrap calibrated tests exhibited superior performance; they attain the type I error in the vast majority of the case scenarios examined and possess nearly indistinguishable empirical power levels. Finally, examples with real data illustrate the performance of the bootstrap calibrated tests. [ABSTRACT FROM AUTHOR]

Count data monitoring has important applications in many fields. However, most of the existing control charts for monitoring count data are parametric. Parametric control charts can be problematic when the underlying parametric distributional assumption does not hold for the particular application. On the other hand, nonparametric control charts do not require such distributional assumptions, and are more desirable in real‐world situations where the underlying distribution cannot be easily described using a parametric distribution. In this paper, we extend the nonparametric control chart for continuous data monitoring proposed by Li to count data monitoring. To guarantee a desired in‐control performance, we further adopt the bootstrap procedure proposed by Gandy and Kvaløy to help determine the control limit of our proposed control chart. Our simulation studies and real data analysis show that the proposed control chart performs well across a variety of settings, and compares favorably with other existing nonparametric control charts for count data. [ABSTRACT FROM AUTHOR]

In this paper, we compare two regression curves by measuring their difference by the area between the two curves, represented by their L 1 -distance. We develop asymptotic confidence intervals for this measure and statistical tests to investigate the similarity/equivalence of the two curves. Bootstrap methodology specifically designed for equivalence testing is developed to obtain procedures with good finite sample properties and its consistency is rigorously proved. The finite sample properties are investigated by means of a small simulation study. [ABSTRACT FROM AUTHOR]

This paper discusses the problem of the mean changes in time series with heavy-tailed AR(p) noise. Firstly, it proposes a modified ratio-type test statistic, and the results show that under the null hypothesis of no mean change, the asymptotic distribution of the modified statistic is a functional of Lévy processes and the consistency under the alternative hypothesis is obtained. However, a heavy-tailed index exists in the asymptotic distribution and is difficult to estimate. This paper uses bootstrap sampling, jackknife sampling, and subsampling to approximate the distribution under the null hypothesis, and obtain more accurate critical values and empirical power. In addition, some results from a small simulation study and a practical example give an idea of the finite sample behavior of the proposed statistic. [ABSTRACT FROM AUTHOR]

Abstract Cylindrical data are bivariate data formed from the combination of circular and linear variables. Identifying outliers is a crucial step in any data analysis work. This paper proposes a new distribution-free procedure to detect outliers in cylindrical data using the Mahalanobis distance concept. The use of Mahalanobis distance incorporates the correlation between the components of the cylindrical distribution, which had not been accounted for in the earlier papers on outlier detection in cylindrical data. The threshold for declaring an observation to be an outlier can be obtained via parametric or non-parametric bootstrap, depending on whether the underlying distribution is known or unknown. The performance of the proposed method is examined via extensive simulations from the Johnson-Wehrly distribution. The proposed method is applied to two real datasets, and the outliers are identified in those datasets. [ABSTRACT FROM AUTHOR]

This paper proposes a generalization of the local bootstrap for periodogram statistics when weakly stationary time series are contaminated by additive outliers. To achieve robustness, we suggest replacing the classical version of the periodogram with the M-periodogram in the local bootstrap procedure. The robust bootstrap periodogram is implemented in the Whittle estimator to obtain confidence intervals for the parameters of a time series model. A finite sample size investigation was conducted to compare the performance of the classical local bootstrap with the one proposed in this paper to estimate 95% confidence intervals for the parameters of autoregressive and seasonal autoregressive time series. The results have shown that the robust estimator is resistant to additive outlier contamination and produces confidence intervals with coverage percentages closer to 95% and lower amplitudes than the ones obtained with the classical estimator, even for small percentages and magnitudes of outliers. It was also empirically observed that when the expected number of outliers is kept constant, the coverage percentages of the confidence intervals of the robust estimators tend to 95% as the sample size increases. An application to the daily mean concentration of particulate matter with a diameter smaller than 10 μ m (PM 10 ) was considered to illustrate the methodologies in a real data context. All the results presented here strongly motivate using the proposed robust methodology in practical situations where additive outliers contaminate weakly stationary time series. [ABSTRACT FROM AUTHOR]

In multiple linear regressions, it is known that least-squares estimates of the parameters are likely to be too large in absolute value and possibly of wrong sign, if explanatory variables are correlated. To reduce the undesirable effects of collinearity, the ridge estimator has been proposed as an alternative method to the least squares estimator. The biggest debate with the ridge estimator is the selection of the regularization parameter. Several methods for the selection of the regularization parameter have been discussed. Although most of these methods are based on minimizing the mean square error of the ridge estimator, bootstrap resampling method is also proposed to provide an optimal regularization parameter which gives an estimate of mean square error of prediction. The purpose of this paper is to provide a comprehensive study of regularization parameter selection methods which consider bootstrap approach as well as estimation and prediction approaches. The paper concludes with application of these procedures to simulation studies and real data. [ABSTRACT FROM AUTHOR]

Several control charts for individual observations are compared. Traditional ones are the well-known Shewhart individuals control charts based on moving ranges. Alternative ones are non-parametric control charts based on empirical quantiles, on kernel estimators, and on extreme-value theory. Their in-control and out-of-control performance are studied by simulation combined with computation. It turns out that the alternative control charts are not only quite robust against deviations from normality but also perform reasonably well under normality of the observations. The performance of the Empirical Quantile control chart is excellent for all distributions considered, if the Phase I sample is sufficiently large. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Parameter estimation is an important component of statistical inference, and how to improve the accuracy of parameter estimation is a key issue in research. This paper proposes a linear Bayesian estimation for estimating parameters in a misrecorded Poisson distribution. The linear Bayesian estimation method not only adopts prior information but also avoids the cumbersome calculation of posterior expectations. On the premise of ensuring the accuracy and stability of computational results, we derived the explicit solution of the linear Bayesian estimation. Its superiority was verified through numerical simulations and illustrative examples. [ABSTRACT FROM AUTHOR]

Post-processing using deep learning algorithms can be conducted to improve accuracy of hydrologic predictions and quantify their uncertainty. In this paper, a revised version of the Local uncertainty estimation model (LUEM-R) and the circular block bootstrap (CBB) method have been used to improve the accuracy of the Variable Infiltration Capacity's (VIC) streamflow simulation and quantify its uncertainty. We used the simulated and observed streamflow at the gauge located in North CAPE Fear basin, USA from the Dayflow dataset. In the LUEM-R method, a combination of Gaussian Mixture Model and Long Short-Term Memory (LSTM) networks, which are able to capture the dependencies in time series, were used to construct the upper and lower prediction limits (PLs) for the 90% confidence level. In the CBB method, a circular block resampling technique was used to account for the dependencies in the time series (CBB-LSTM). The improved streamflow, calculated as the mean of the LSTM outputs for 200 bootstrap realizations, showed a very high correlation with observations, with coefficient of determination values of 0.97 and 0.87 for the training and testing periods, compared to the 0.77 and 0.74 values for the initial VIC simulations. For the CBB-LSTM method, the 90% PLs were constructed by fitting the best distribution at each time step, accordingly. The PLs bracketed 90% and 70% of observations in the training and testing periods, while being significantly narrower than the LUEM-R bands, which contained 92 and 91 percent of observations in the training and testing periods. Ordinary bootstrapping was also conducted using the Random Forest model (OB-RF). Comparison of the results indicates the superiority of CBB-LSTM method to the OB-RF in improving the accuracy and quantifying the uncertainties in hydrological model simulations. Overall, the CBB-LSTM was successful in improving the deterministic accuracy of VIC model simulations and quantifying its uncertainty. Also, the LUEM-R method could be efficiently utilized in quantification of uncertainty of VIC model simulations. [ABSTRACT FROM AUTHOR]

This paper presents a novel estimator for a nonstandard restriction to both symmetry and low rank in the context of high-dimensional cointegrated processes. Furthermore, we discuss rank estimation for high-dimensional cointegrated processes by restricted bootstrapping of the Gaussian innovations. We demonstrate that the classical rank test for cointegrated systems is prone to underestimating the true rank and demonstrate this effect in a 100-dimensional system. We also discuss the implications of this underestimation for such high-dimensional systems in general. Also, we define a linearized Kuramoto system and present a simulation study, where we infer the cointegration rank of the unrestricted p\times p system and successively the underlying clustered network structure based on a graphical approach and a symmetrized low rank estimator of the couplings derived from a reparametrization of the likelihood under this unusual restriction. [ABSTRACT FROM AUTHOR]

Multivariate statistical process control (MSPC) was developed for the monitoring of variables that are either all numerical or all categorical. In the present paper, we describe a nonparametric control scheme that can be used to monitor a mixture of numerical and categorical variables simultaneously. It integrates Principal Component Analysis Mix (PCA Mix), a multivariate statistical tool, with the conventional Hotelling T2 chart. To estimate the control limit for the PCA Mix-based T2 statistic, two nonparametric approaches – kernel density estimation (KDE) and bootstrap – are employed, because of the unknown nature of the underlying distribution. The simulation results demonstrate that with an appropriate number of principal components, both bootstrap and KDE exhibit convincing performance in terms of generating the same, or nearly the same, number of false alarms (ARL0) as expected, and being able to detect process shifts efficiently (ARL1). Compared with bootstrap, KDE is shown to work better with small sample sizes (n < 800) and to be slightly more sensitive to small shifts. However, the results also show the instability of the estimated nonparametric control limit when highly imbalanced categorical variables are included, which indicates the need for further research on this topic. [ABSTRACT FROM AUTHOR]

For checking time series models, the Ljung–Box, Li–Mak and Zhu–Wang statistics play an important role, which use the Pearson's correlation coefficient to implement (squared) residual (partial) autocorrelation tests. In this paper, we replace the Pearson's correlation coefficient with a new rank correlation coefficient and propose a new test statistic to conduct diagnostic checks for residuals in autoregressive moving average models, autoregressive conditional heteroscedasticity models and integer-valued time series models, respectively. We conduct simulations to assess the performance of the new test statistic, and compare it with existing ones, and the results show the superiority of the proposed one. We use three real examples to exhibit its usefulness. [ABSTRACT FROM AUTHOR]

In this study, hypothesis test is investigated based on Bootstrap sample selection methods to compare more than two population means under Ranked Set Sampling. Bootstrap sample selection methods are obtained by adapting Hui’s sample selection methods for confidence interval. We also compare these adapted methods with bootstrap simple random sampling and bootstrap ranked set sampling methods using simulation study. Simulation study shows that adapted methods which proposed in this paper perform quite well. [ABSTRACT FROM AUTHOR]

This paper builds on the recently proposed prediction test for muliple endpoints. The prediction test combines information across multiple endpoints while accounting for the correlation between them. The test performs well with small samples relative to the number of endpoints of interest and is flexible in the hypotheses across the individual endpoints that can be combined. The prediction test addresses a global hypothesis that is of particular interest in early-stage studies and can be used as justification for continuing on to a larger trial. However, the prediction test has several limitations which we seek to address. First, the prediction test is overly conservative when both the effect sizes across all endpoints and the number of endpoints are small. By using a parametric bootstrap to estimate the null distribution, we show that the test achieves the nominal error rate in this situation and increases the power of the test. Second, we provide a framework to allow for predictions of a difference on one or more endpoints. Finally, we extend the test with a composite null hypothesis that allows for different null hypothesized predictive abilities across the endpoints which can be especially useful if the study contains both familiar and novel endpoints. We use an example from a physical activity trial to illustrate these extensions. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of identifying modes or density bumps in multivariate angular or circular data, which have diverse applications in fields like medicine, biology and physics. We focus on the use of topological data analysis and persistent homology for this task. Specifically, we extend the methods for uncertainty quantification in the context of a torus sample space, where circular data lie. To achieve this, we employ two types of density estimators, namely, the von Mises kernel density estimator and the von Mises mixture model, to compute persistent homology, and propose a scale‐space view for searching significant bumps in the density. The results of bump hunting are summarised and visualised through a scale‐space diagram. Our approach using the mixture model for persistent homology offers advantages over conventional methods, allowing for dendrogram visualisation of components and identification of mode locations. For testing whether a detected mode is really there, we propose several inference tools based on bootstrap resampling and concentration inequalities, establishing their theoretical applicability. Experimental results on SARS‐CoV‐2 spike glycoprotein torsion angle data demonstrate the effectiveness of our proposed methods in practice. [ABSTRACT FROM AUTHOR]

The use of longitudinal finite mixture models such as group-based trajectory modeling has seen a sharp increase during the last few decades in the medical literature. However, these methods have been criticized, especially because of the data-driven modeling process, which involves statistical decision-making. In this paper, we propose an approach that uses the bootstrap to sample observations with replacement from the original data to validate the number of groups identified and to quantify the uncertainty in the number of groups. The method allows investigation of the statistical validity and uncertainty of the groups identified in the original data by checking to see whether the same solution is also found across the bootstrap samples. In a simulation study, we examined whether the bootstrap-estimated variability in the number of groups reflected the replicationwise variability. We evaluated the ability of 3 commonly used adequacy criteria (average posterior probability, odds of correct classification, and relative entropy) to identify uncertainty in the number of groups. Finally, we illustrate the proposed approach using data from the Quebec Integrated Chronic Disease Surveillance System to identify longitudinal medication patterns between 2015 and 2018 in older adults with diabetes. [ABSTRACT FROM AUTHOR]

We describe software for stochastic programming that uses only sampled data to obtain both a consistent sample-average solution and a consistent estimate of confidence intervals for the optimality gap using bootstrap and bagging. The underlying distribution whence the samples come is not required. History: Accepted by Ted Ralphs, Area Editor for Software Tools. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0253) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0253). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

In this paper, we consider the beta prime regression model recently proposed in the literature, which is tailored to situations where the response is continuous and restricted to the positive real line with skewed and long tails and the regression structure involves regressors and unknown parameters. We consider two different strategies of bias correction of the maximum-likelihood estimators for the parameters that index the model. In particular, we discuss bias-corrected estimators for the mean and the dispersion parameters of the model. Furthermore, as an alternative to the two analytically bias-corrected estimators discussed, we consider a bias correction mechanism based on the parametric bootstrap. The numerical results show that the bias correction scheme yields nearly unbiased estimates. An example with real data is presented and discussed. [ABSTRACT FROM AUTHOR]

Rehabilitation training for patients with limb activity dysfunction and sub-healthy state has gradually shifted from therapies to strategies with remote assistance. Stochastic configuration networks (SCNs) are characterized by a structure that varies with task complexity, making them ideal for use as the lightweight AI activity recognition model in a remote rehabilitation training system. Given an imbalanced data classification and large-scale data analytics task, the original SCN classifiers may fail to provide satisfied performance. In this paper, we propose two solution that are Bagging SCNs and Boosting SCNs for HAR based on SCNs. Bagging SCNs use the bootstrap method to generate balanced subsets to reduce the influence caused by imbalance dataset. Then, multiple SCNs models are trained in parallel, followed by the identification of the best ensemble model through validation sets. Boosting SCNs employ forward stagewise additive modeling and utilize the SAMME algorithm to minimize the multi-class exponential loss for multi-class classification. This algorithm progressively enhances the base learner's focus on previously misclassified instances from previous rounds, ultimately lowering the misclassification rate. The activity datasets of three groups of tests are collected by using a self-built experimental platform. Our experiments compare the performance of two Ensemble SCNs with original SCNs, Convolutional Neural Networks, Long Short-Term Memory, Gradient Boosting Decision Tree(GBDT) and Support Vector Classifier. Results in the performance of two Ensemble SCNs demonstrate that our proposed algorithm has good potential to be applied for HAR algorithm. [ABSTRACT FROM AUTHOR]

It is well known that the variances of the least squares estimates are large and they can be far away from their true values in the case of multicollinearity. Therefore, the ridge regression method can be used as an alternative to the least squares method. However, the ridge estimator has a disadvantage that its distribution is unknown, so only asymptotic confidence intervals are obtained. The purpose of this paper is to study the impact of several ridge regularization parameters on the mean interval lengths of the confidence intervals and coverage probabilities constructed by the ridge estimator. A bootstrap method for the selection of ridge regularization parameter is used as well as the parametric methods. In order to compare the confidence intervals, standard normal approximation, student-t approximation and bootstrap methods are used and comparison is illustrated via real data and simulation study. The simulation study shows that the bootstrap choice of ridge regularization parameter yields narrower standard normal approximated confidence intervals than the PRESS choice of ridge regularization parameter but wider standard normal approximated, student-t approximated and bootstrap confidence intervals than the GCV choice of ridge regularization parameter. [ABSTRACT FROM AUTHOR]

In this paper, the one-sided hypothesis testing and interval estimation problems for the fixed effect and variance component functions are considered in the skew-normal unbalanced heteroscedastic one-way classification random effects model. Firstly, the Bootstrap approach is used to establish test statistic for fixed effect. Secondly, the test statistics and confidence intervals for variance component functions are constructed by Bootstrap approach and generalized approach, and their theoretical properties are discussed. The Monte Carlo simulation results indicate that the Bootstrap approach performs better than the generalized approach in most cases. Finally, the above approaches are illustrated with two real examples of the annual average concentrations of fine particulate matter and nitrogen dioxide. [ABSTRACT FROM AUTHOR]

An important problem in directional statistics is to test the null hypothesis of a common mean direction for several populations. The Analysis of Variance (ANOVA) test for vectorial data may be used to test the hypothesis of the equality of the mean directions for several von Mises-Fisher populations. As this test is valid only for large concentrations, we propose in this paper to apply the resampling techniques of bootstrap and permutation to the ANOVA test. We carried out an extensive simulation study in order to evaluate the performance of the ANOVA test with the resampling techniques, for several sphere dimensions and different sample sizes and we compare with the usual ANOVA test for data from von Mises-Fisher populations. The purpose of this simulation study is also to investigate whether the proposed tests are preferable to the ANOVA test, for low concentrations and small samples. Finally, we present an example with spherical data. [ABSTRACT FROM AUTHOR]

The primary objective of this paper is to assess the effects of ad music attitude (Aam) on ad attitude (Aad), brand attitude (Ab), and purchase intention (PI). Further, this article intends to test the mediating role of Aad and Ab between Aam and PI. The bootstrap method in AMOS 20 was adopted to test the hypotheses. The finding indicates that Aam invokes Aad, which influences Ab, and in turn, invokes PI. The result suggests a hierarchical relationship between Aam, Aad, Ab, and PI. Subsequently, it supports the central hypothesis of the serial mediation role of Aad and Ab between Aam and PI. This research adds to the ad and marketing literature by empirically examining the relationship of Aam with Aad, Ab, and PI; proposes a multiple and serial mediation model to study the relationships. Knowing that attitudes (music, ad, and brand) can have a significant and positive relationship and can, in some cases, mediate each other allows advertisers a more efficient and effective way to advertise both traditionally and digitally to attain PI. [ABSTRACT FROM AUTHOR]

The Kronecker product covariance structure provides an efficient way to model the inter-correlations of matrix-variate data. In this paper, we propose test statistics for the Kronecker product covariance matrix based on linear spectral statistics of renormalized sample covariance matrices. A central limit theorem is proved for the linear spectral statistics, with explicit formulas for the mean and covariance functions, thereby filling a gap in the literature. We then show theoretically that the proposed test statistics have well-controlled size and high power. We further propose a bootstrap resampling algorithm to approximate the limiting distributions of the associated linear spectral statistics. Consistency of the bootstrap procedure is guaranteed under mild conditions. The proposed test procedure is also applicable to the Kronecker product covariance model with additional random noise. In our simulations, the empirical sizes of the proposed test procedure and its bootstrapped version are close to the corresponding theoretical values, while the power converges to |$1$| quickly as the dimension and sample size increase. [ABSTRACT FROM AUTHOR]

In this paper, we propose a likelihood ratio test for a change in persistence of a time series. We consider the null hypothesis of a constant persistence I(1) and an alternative in which the series changes from a stationary regime to a unit root regime or vice versa. Both known and unknown break dates are analyzed. Moreover, we consider a modification of a lag length selection procedure which provides better size control over various data generation processes. The bootstrap with recoloring also improves size. In general, our likelihood ratio-based tests show the best finite sample properties from all persistence change tests that use the null hypothesis of a unit root throughout. [ABSTRACT FROM AUTHOR]

This paper surveys the increasing use of statistical approaches in non-parametric efficiency studies. Data Envelopment Analysis (DEA) and Free Disposable Hull (FDH) are recognized as standard non-parametric methods developed in the field of operations research. Kneip et al. (Econom Theory, 14:783–793, 1998) and Park et al. (Econom Theory, 16:855–877, 2000) develop statistical properties of the variable returns-to-scale (VRS) version of DEA estimators and FDH estimators, respectively. Simar & Wilson (Manag Sci 44, 49–61, 1998) show that conventional bootstrap methods cannot provide valid inference in the context of DEA or FDH estimators and introduce a smoothed bootstrap for use with DEA or FDH efficiency estimators. By doing so, they address the main drawback of non-parametric models as being deterministic and without a statistical interpretation. Since then, many articles have applied this innovative approach to examine efficiency and productivity in various fields while providing confidence interval estimates to gauge uncertainty. Despite this increasing research attention and significant theoretical and methodological developments in its first two decades, a specific and comprehensive bibliometric analysis of bootstrap DEA/FDH literature and subsequent statistical approaches is still missing. This paper thus, aims to provide an extensive overview of the key articles and their impact in the field. Specifically, in addition to some summary statistics such as citations, the most influential academic journals and authorship network analysis, we review the methodological developments as well as the pertinent software applications. [ABSTRACT FROM AUTHOR]

We explore an exchangeably weighted bootstrap of the general function-indexed empirical U-processes in the Markov setting, which is a natural higher-order generalization of the weighted bootstrap empirical processes. As a result of our findings, a considerable variety of bootstrap resampling strategies arise. This paper aims to provide theoretical justifications for the exchangeably weighted bootstrap consistency in the Markov setup. General structural conditions on the classes of functions (possibly unbounded) and the underlying distributions are required to establish our results. This paper provides the first general theoretical study of the bootstrap of the empirical U-processes in the Markov setting. Potential applications include the symmetry test, Kendall's tau and the test of independence. [ABSTRACT FROM AUTHOR]

Air cargo is an important strategic resource of country and plays an indispensable role in domestic and international trade. Scientific forecasting of air cargo demand is an important basis for airlines to make infrastructure planning and overall investment decisions. Aiming at the uncertainty of air cargo volume data, this paper introduced Bootstrap method for uncertainty estimation and proposed an interval prediction method based on decomposition integration from the practical needs. Specifically, this paper decomposed the historical data by Seasonal and Trend Decomposition using Loess (STL) method firstly, then forecasted the trend and seasonal components by Support Vector Regression (SVR) and Seasonal Autoregressive Integrated Moving Average (SARIMA), respectively. Thirdly, this paper extracted and resampled the white noise component by Bootstrap method. Finally, the prediction results were integrated and reconstructed with the processed white noise to quantify uncertainty using quantile construction intervals. The experimental results of cargo data from two hub airports in China show that the constructed interval can effectively quantify the uncertainty in combination with the predicted results, which provides a novel research idea for probabilistic interval prediction. [ABSTRACT FROM AUTHOR]

Summary: Most modern articles in the palaeomagnetism literature are based on statistics developed by Fisher's 1953 paper 'Dispersion on a sphere', which assumes independent and identically distributed (iid) spherical data. However, palaeomagnetic sample designs are usually hierarchical, where specimens are collected within sites and the data are then combined across sites to calculate an overall mean direction for a geological formation. The specimens within sites are typically more similar than specimens between different sites, and so the iid assumptions fail. This article has three principal goals. The first is to review, contrast and compare both the statistics and geophysics literature on the topic of analysis methods for clustered data on spheres. The second is to present a new hierarchical parametric model, which avoids the unrealistic assumption of rotational symmetry in Fisher's 1953 paper 'Dispersion on a sphere' and may be broadly useful in the analysis of many palaeomagnetic datasets. To help develop the model, we use publicly available data as a case study collected from the Golan Heights volcanic plateau. The third goal is to explore different methods for constructing confidence regions for the overall mean direction based on clustered data. Two bootstrap confidence regions that we propose perform well and will be especially useful to geophysics practitioners. [ABSTRACT FROM AUTHOR]