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In this paper, the stress–strength reliability $ R_{s,k} $ R s , k of a multicomponent s-out-of-k system for exponentiated Gumbel distribution is considered. An s-out-of-k system means a system with total k components and the system can survive only when atleast s of the total components function properly. The ability of the system to overcome the experiencing stress with its strength is termed as its stress–strengh reliability. The maximum likelihood estimator and Bayes estimator for $ R_{s,k} $ R s , k are obtained. The Bayes estimators are obtained using Markov chain Monte Carlo(MCMC) method under both symmetric and asymmetric loss functions. The loss functions we considered are squared error loss function, LINEX loss function and entropy loss function. The asymptotic, bootstrap and highest posterior density(HPD) confidence intervals for $ R_{s,k} $ R s , k are also obtained. A simulation study is conducted for evaluating the efficiency of the estimators derived in this paper. Real data sets are also considered for illustration. [ABSTRACT FROM AUTHOR]

Most of the control charts in the literature focus on detecting constant mean shifts. In practice, dynamic and time-varying process mean shifts are prevalent in the monitoring of feedback-control and autocorrelated processes. The cumulative score (CUSCORE) charts have been proposed in the literature to detect dynamic and time-varying process shifts. One of such control charts is a reference-free CUSCORE (called RFCS-I) chart that may detect unknown patterned mean shifts effectively. In this paper, single and dual CUSCORE charts are developed to enable an efficient detection of unknown patterned mean shifts. The developed single CUSCORE chart, called the RFCS-II chart, is based on the control charting structure of the Crosier CUSUM (called CU-II) chart. Additionally, two RFCS-I charts are integrated with reflecting boundaries, while an integration of two RFCS-II charts is also made, to develop the dual RFCS-I (DRFCS-I) and dual RFCS-II (DRFCS-II) charts, respectively. In addition, the RFCS-I and RFCS-II charts are integrated to propose the mixed dual reference-free CUSCORE chart, called the MDRFCS chart. In essence, four CUSCORE charts, i.e. the RFCS-II, DRFCS-I, DRFCS-II and MDRFCS charts are suggested in this paper. The Monte Carlo simulation and a real application illustrate the superiority of these developed CUSCORE charts over their existing counterparts when detecting patterned mean shifts in terms of zero-state and steady-state relative mean indexes. [ABSTRACT FROM AUTHOR]

This paper presents a new method for the feature screening of ultra-high dimensional data with response missing at random. The distribution function of the missing response is completed by imputation technology, and then the distance correlation between the imputed distribution function of response and the distribution function of covariate is used as an index for feature screening. The proposed method has the following advantages. First, it is a nonparametric model-free method, and can detect the nonlinear relationship between variables. Second, it is robust to covariates with outliers and heavy-tailed distributions. Third, it can deal with multi-dimensional response variables directly. Under certain assumptions, this paper demonstrates the sure screening and ranking consistency properties. Simulation studies are conducted to examine the performance of the proposed procedure and to compare with existing methods. Finally, our method is applied to the data analysis of diffuse large B-cell lymphoma. [ABSTRACT FROM AUTHOR]

Time series of proportions are often encountered in applications such as ecology, environmental science and public health. Strategies for such data include linear regression after logistic transformation. Though easy to fit, the transformation approach renders covariate effects uninterpretable on the scale on which they were observed owing to Jensen's inequality. An alternative to the transformation approach has been to directly model the response via the beta distribution. In this paper, we extend zero-inflated beta regression models for independent proportions to time series data that is bounded over the unit interval and that may take on zero values. Estimation is within the partial-likelihood framework and is computationally feasible to implement. We outline the asymptotic theory of our maximum partial likelihood estimators under mild regularity conditions and investigate their bias and variability using simulation studies. The utility of our method is illustrated using two real data examples. [ABSTRACT FROM AUTHOR]

The Buckley–James method for the classical accelerated failure time model has been extended to accommodate heteroscedastic survival data in two ways. The first is the weighted least squares method [Yu et al. Weighted least-squares method for right-censored data in accelerated failure time model. Biometrics. 2013;69:358–365], which estimates the heteroscedasticity nonparametrically, while the second is the local Buckley–James method [Pang et al. Local Buckley–James estimation for heteroscedastic accelerated failure time model. Stat Sin. 2015;25:863–877], which uses local Kaplan–Meier method to estimate the heteroscedasticity. However, no comparisons have been done for these two methods. Furthermore, there is no hypothesis testing procedure for this heteroscedastic accelerated failure time model. This paper is then aimed to fill these two gaps to compare the two methods theoretically and numerically with extensive simulation studies. In addition, we propose a class of hypothesis tests for the parameters to provide a complete procedure for analysing heteroscedastic survival data. Two real data examples are used for practical illustration of the comparison and the new proposed tests. [ABSTRACT FROM AUTHOR]

In this paper, we study the estimation problem about the regression coefficients of a multivariate regression model with measurement errors under some uncertain restrictions. Specifically, we propose the unrestricted estimator (UE) and three restricted estimators (REs), and prove that they are all consistent for the true coefficients. We derive the asymptotic distributions of the proposed estimators under the sequence of local alternative restrictions. We also propose shrinkage estimators (SEs) to address the problem of the uncertainty of the restrictions. In addition, we establish the asymptotic distributional risk (ADR) of the proposed estimators and compare the risk performance of these estimators. It is established that the REs perform better than the UE only near the restriction, while they perform poorly as one moves farther away from the restriction. We also prove that SEs dominate the UE. These theoretical results are confirmed by simulations. [ABSTRACT FROM AUTHOR]

A two-sided sequential probability ratio test (SPRT) control chart for monitoring the mean of a normal process is proposed in this paper. Its mechanism is based on the SPRT for the mean of a normal distribution that is extended for a two-sided alternative. The exact statistical performance measures of this chart are obtained using a Markov chain approach. An approach to design the chart such that it has a specified in-control performance and the optimal out-of-control performance for detecting a mean shift of a particular size is provided. The statistical performance of this chart is numerically compared with that of various competing charts in the existing literature. It is found that the proposed chart outperforms all these charts for detecting a mean shift of any size. An example to illustrate the mechanism of the chart is provided. [ABSTRACT FROM AUTHOR]

Due to the quick identification of the root causes for an out-of-control process, the estimation of exact time of a process change would be helpful thing for the process improvement. In contrast to the typical normal assumption, this study realizes that a process may follow a skewed Maxwell distribution. In this paper, using maximum likelihood estimation, a considerably efficient change point model is proposed for $ V $ V control chart which underlying distribution is Maxwell distribution. The required chart statistics are calculated with its distributional properties. The proposed method is used when $ V $ V control chart signals a change in a process parameter. The proposed method, when used with $ V $ V control chart would be helpful for process engineers both in controlling and identifying a permanent step change in a process scale parameter. An illustrative example is given to understand the use of the proposed method. [ABSTRACT FROM AUTHOR]

The Lilliefors test of normality is a popular and easy-to-explain method for testing whether a sample comes from a normal distribution. Unfortunately, since it relies on the sample mean and sample standard deviation for estimating the parameters of the normal distribution, the Lilliefors test is quite sensitive to the presence of outliers. Contrarily to what could be expected, the substitution of the estimators of location and scale by robust alternatives still does not suffice for obtaining a robust method when either the number of outliers or the sample size is large. In this paper, we propose an actual robust alternative relying on classical and data-driven trimming techniques. The presented test depends on the choice of a subsetting technique, of which we explore three possibilities, and of one parameter, which models the robustness of the test in the presence of outliers. As expected, the choice of parameter is a delicate issue since the gain in robustness comes at the price of a reduced power against some types of alternatives. [ABSTRACT FROM AUTHOR]

Statistical inference for high-dimensional survival data is important for obtaining valid scientific results in many research areas, including biomedical studies and financial risk management. In this paper, a novel framework for feature selection in Cox model is proposed, which achieves false discovery rate (FDR) control asymptotically. The key step is to construct a sequence of ranking statistics based on two independent estimators of the regression coefficients. The FDR control is reached by choosing a data-driven threshold along the ranking of symmetric-based statistics. The de-sparsified estimator and uneven data splitting strategy are employed to improve the robustness of variable selection results and the power in finite sample analysis. We establish the asymptotic FDR control property for the proposed approach at any designated level. Extensive simulation studies and an empirical application on a P2P loan dataset confirm the robustness of the proposed method in FDR control, and show that it often leads to higher power among competitors. [ABSTRACT FROM AUTHOR]

There are numerous phenomena in real world that their practical modeling in mathematics language deals with differential equations. Stochastic terms have significant roles in estimating behavior of these events such as machine tool vibrations, biology, traffic dynamics, neural networks and so on, it cannot be reasonable to consider an event without its past information, and it ends up with equations including time delays. The numerical solution of stochastic delay differential equations has always been of interest to researchers. In this paper, by using scaling function of the Daubechies wavelet, a collocation method is presented to solve a class of stochastic delay differential equations and it is tried to demonstrate the advantages of using this type of wavelet. Convergence of the method is provided and numerical experiments are reported to show application of the method in practice. [ABSTRACT FROM AUTHOR]

Phylogenetic Trees are critical in human genome research for investigating human evolution and identifying disease-associated genetic markers. New high-throughput genome sequencing technologies raise an urgent need to develop statistical methods that can construct phylogenetic trees from long genome sequences with quick computation speeds, while considering various biological complexities. Though an ancestral mixture model has been proposed [Chen SC, Lindsay BG. Building mixture trees from binary sequence data. Biometrika. 2006;93(4):843–860. doi: 10.1093/biomet/93.4.843] to this end by allowing genetic mutations over generations, another essential evolution factor, genetic recombination, is missed. Therefore, in this paper, we develop a novel genetic recombination model for tree construction and propose to use Markov chain composite likelihood (MCCL) to make model estimation computationally feasible. To further reduce computation complexity, a hierarchical estimator is constructed to estimate unknown ancestral distributions through MCCL. Simulation studies and real data example show that our proposed methods perform well and fast, so have the potential for implementation in long sequence genome data. [ABSTRACT FROM AUTHOR]

Compositional data (CoDa) often appear in various fields such as biology, medicine, geology, chemistry, economics, ecology and sociology. Although existing Dirichlet and related models are frequently employed in CoDa analysis, sometimes they may provide unsatisfactory performances in modelling CoDa as shown in our first real data example. First, this paper develops a multivariate compositional inverse Gaussian (CIG) model as a new tool for analysing CoDa. By incorporating the stochastic representation (SR), the expectation–maximization (EM) algorithm (aided by a one-step gradient descent algorithm) can be established to solve the parameter estimation for the proposed distribution (model). Next, zero observations may be often encountered in the real CoDa analysis. Therefore, the second aim of this paper is to propose a new model (called as ZCIG model) through a novel mixture SR based on both the CIG random vector and a so-called zero-truncated product Bernoulli random vector to model CoDa with zeros. Corresponding statistical inference methods are also developed for both cases without/with covariates. Two real data sets are analysed to illustrate the proposed statistical methods by comparing the proposed CIG and ZCIG models with existing Dirichlet and logistic-normal models. [ABSTRACT FROM AUTHOR]

In this paper, the asymptotic normality and strong consistency for M estimators of the unknown regression coefficients in classical linear models are established under the assumptions that the errors are identically distributed φ-mixing random variables. The results obtained in this paper generalize the corresponding ones of Chen and Zhao [M-methods in linear model. Shanghai: Scientific and Technical Publishers; 1996] and Zhao [Strong consistency of M-estimates in linear model. Sci China Ser A. 2002;45:1420–1427] for independent errors. Finally, the simulation study is provided to verify the finite sample performance of the theoretical results and a real example is analysed for illustration. [ABSTRACT FROM AUTHOR]

This paper presents interval estimation for the population mean and coefficient of variation in a two-parameter exponential distribution. The new generalized pivot, profile likelihood function and likelihood ratio statistic are derived and used to construct the confidence intervals. A highlight of this paper is that the generalized and likelihood ratio confidence intervals for the mean and coefficient of variation perform well in terms of coverage probability in many cases. Finally, two real-data applications on the air pollution of particulate matter (PM2.5) and the renewable energy through wind power of Thailand are used for illustration purposes. [ABSTRACT FROM AUTHOR]

The combined effect of two real-world-occurring phenomena: 'measurement errors' and 'autocorrelation between observations' has rarely been investigated. In this paper, it will be investigated for the first time on 'adaptive' and/or 'simultaneous monitoring' charts and also for the first time by using the multivariate linearly covariate measurement errors and VARMA (vector mixed autoregressive and moving average) autocorrelation models, and Markov chains-based performance measures. In addition, this paper for the first time proposes a skip-sampling strategy in an ARMA/VARMA model for alleviating the autocorrelation effect. To do so, we add the above-mentioned measurement errors and autocorrelation models to a recently developed adaptive max-type chart. Then, we develop a Markov chain model to compute the performance measures. After that, extensive numerical analyses will be performed to investigate their combined effect as well as some methods to alleviate their negative effects. Finally, an illustrative example involving a real industrial case will be presented. [ABSTRACT FROM AUTHOR]

In this paper we extend the family of test proposed by Majumder and Mitra [Detecting trend change in failure functions-an L-statistic approach. Stat Pap. 2019;62:31–52. doi: ] for testing exponentiality against bathtub (BT) failure rate (upside down bathtub (UBT)) to randomly right censored case. We derive the asymptotic distribution of the test statistic and using Monte Carlo simulation we obtain the empirical powers for certain alternative distributions. As a special case the asymptotic distribution of the test statistic proposed by Park [Testing whether failure rate changes its trend. IEEE Trans Reliab. 1988;37(4):375–378. doi: ] is obtained. Finally some examples of real life data are given for illustrative purpose. [ABSTRACT FROM AUTHOR]

This paper investigates the E-Bayesian and hierarchical Bayesian estimations of shape parameter and reliability function of Kumaraswamy generalized distribution based on upper record values. The classical estimation method is utilized to deduce the maximum likelihood estimation of unknown parameter and reliability function. Bayesian estimates are derived by using conjugate Gamma prior distributions under quadratic and general entropy loss functions. Furthermore, assuming that hyper-hyperparameters obey three prior distributions, the E-Bayesian estimates of unknown parameters and reliability functions are obtained. The hierarchical Bayesian estimates are obtained by using hierarchical prior distributions. We also explore some characteristics and size relationships of E-Bayesian and hierarchical Bayesian estimations. The performance of E-Bayesian, Hierarchical Bayesian, Bayesian, and maximum likelihood estimations is compared based on the minimum mean square error criterion. Finally, the proposed estimation methods are applied to evaluate the reliability of the specimen under ultrasonic fatigue testing, and the results align with their structures and profiles. [ABSTRACT FROM AUTHOR]

The Lomax distribution is one of the well-known distributions that is used to fit heavy-tailed data. In this paper, we investigate the estimation of Shannon entropy of the Lomax distribution using noninformative priors. Some important priors including Jeffreys prior, reference priors and probability matching priors are presented. We demonstrate that the reference and matching priors for the Lomax entropy do not match the reference and probability matching priors of the Lomax parameters, regardless of which parameter of interest is considered. The propriety and the existence of the expectation of the posterior under each prior are validated, respectively. A simulation study is conducted to assess the frequentist performance of the proposed Bayesian estimates in terms of the mean squared error and coverage probability. Finally, the approach is applied to three real data sets for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the stress-strength reliability estimation under balanced joint Type-II progressive censoring scheme for independent samples from two different populations. We simultaneously place two independent samples where the experimental units follow Weibull distributions with common shape parameter β and different scale parameters α, λ, respectively. The maximum likelihood estimators of the unknown parameters are derived. Further, the Bayesian inference is considered using Lindley's approximation and Gibbs sampling method. Extensive simulations are performed to see the effectiveness of the proposed estimation methods. Further, we derive the optimal censoring scheme in the Bayesian framework by using the variable neighbourhood search method proposed by [Bhattacharya et al. On optimum life-testing plans under type-ii progressive censoring scheme using variable neighbourhood search algorithm. Test. 2016;25(2):309–330]. Further, some simulation schemes are provided to compare the performances of the estimations under the jointly censored samples versus two separate censored samples. [ABSTRACT FROM AUTHOR]

In this paper, a new threshold INAR(1) model based on modified negative binomial operator with random coefficient is proposed. Basic probabilistic and statistical properties of this process are established. Then the conditional least squares (CLS) and the conditional maximum likelihood (CML) methods are applied to estimate the model parameters when the threshold value is known or not. The asymptotic properties of the CLS-estimator and the CML-estimator are also been discussed. A method to test the constancy of the autoregressive parameters is provided. As an illustration, a simulation study is conducted to illustrate the performances of these estimators and present an empirical analysis of monthly counts of break and enter non-dwelling in Bellingen. [ABSTRACT FROM AUTHOR]

In surveys, successive sampling is generally considered to study the same characteristic from one occasion to another so that the change in characteristics over time can be further studied. This paper presents a class of estimators using a novel approach to estimate population mean on two occasions under successive sampling. We have carried out numerical study and simulation study to validate the significance of the proposed class and its members. We have used an optimum unmatched proportion of each class or estimator to compute their respective mean square error during simulation, while other studies considered some fixed value for unmatched units. For large population, the suggested estimation technique is always better for survey practitioners than others. [ABSTRACT FROM AUTHOR]

Machine learning has developed rapidly and involves many fields, such as signal detection and biological research. However, systems may exist outliers caused by the malicious violation of the attacker during the learning process, which makes machine learning instable and unreliable. Therefore, building a trustworthy model to meet robustness has become an urgent research topic. In this paper, we propose the trustworthy regularized Huber regression by Huber loss and decomposable regularizer under the mean shift model, which can identify and eliminate impacts on outliers and heavy-tailed errors. We establish the consistency and convergence rate of the regularized Huber estimators. The asymptotic property of outliers support recovery is explored in term of false and true discovery rates. Then we design an efficient algorithm by combining the alternating minimization and accelerated proximal gradient method to solve the trustworthy regularized Huber regression. Finally, extensive comparisons on simulation and real datasets demonstrate the superior performances. [ABSTRACT FROM AUTHOR]

In this paper, we extend the optional randomized response technique (ORRT) developed by Chaudhuri and Mukerjee [Optionally randomized response techniques. Bull. Calcutta Statist. Assoc. 1985;34:225–230; Randomized response: theory and techniques. New York: Marcel Dekker, Inc.; 1988] to the situation of estimating the proportion of two sensitive characteristics and their overlap. Lee, Sedory and Singh [Estimating at least seven measures of qualitative variables from a single sample using randomized response technique. Stat Prob Lett. 2013;83(1):399–409; Estimation of odds ratio, attributable risk, relative risk, correlation coefficient and other parameters using randomized response techniques. Behaviormetrika. 2021;48:371–392.] have shown that their crossed model performs better than their simple model from an efficiency point of views. Here we investigated a further improvement in the crossed model along the lines of Chaudhuri and Mukerjee [Optionally randomized response techniques. Bull. Calcutta Statist. Assoc. 1985;34:225–230; Randomized response: theory and techniques. New York: Marcel Dekker, Inc.; 1988]. New unbiased estimators are proposed, their variance expressions are derived and estimators of variances are suggested. Lastly, we carry out a simulation study to investigate the behaviour of the proposed estimators with respect to their competitors. [ABSTRACT FROM AUTHOR]

This paper introduces a robust procedure for controlling the false discovery rate utilizing empirical likelihood. Traditional approaches assume a normal or parametric distribution as the null distribution. However, it may be challenging to constrain the null distribution within specific parametric models. We focus on the cases where the null distribution may not precisely follow a normal distribution. Multiple testing procedures based on exact normality can lead to misleading outcomes. To address this issue, we adopt the empirical likelihood to estimate the null distribution. Additionally, we introduce the concept of a pilot distribution to establish constraints on the null distribution, which aids in estimating the empirical null distribution. We present a fast algorithm and provide theoretical justification for its efficiency. Furthermore, simulation studies demonstrate that our method outperforms existing approaches in controlling the false discovery rate. We also include examples involving gene expression data and compare the performance of different methods. [ABSTRACT FROM AUTHOR]

Over the years, acceptance sampling plans have been crucial to quality assurance in manufacturing. Sample plans are designed using operating characteristic curve conditions to safeguard producers and customers. We propose a conditional probability-based Bayesian generalized multiple-dependent state sampling technique in this paper. The technique relies on Gamma-Poisson distribution. Other performance indicators and acceptance probability are calculated. Also, the new plan's operational method is discussed. The proposed technique is also compared to current attribute sampling schemes for efficacy. Optimal plan parameters for the plan's economic structure are also generated, adding managerial insights to the suggested plan. The entire cost study showed that the suggested plan is cheaper than existing sample plans under identical conditions. To account for inspection flaws, the plan is adjusted. We examine how Type I and Type II errors affect sampling plan outcomes. The plan is demonstrated with numerical examples and a data-driven application. [ABSTRACT FROM AUTHOR]

For the functional linear models in which the dependent variable is functional and the predictors are scalar, robust regularization for simultaneous variable selection and regression parameter estimation is an important yet challenging issue. In this paper, we propose two types of regularized robust estimation methods. The first estimator adopts the ideas of reproducing kernel Hilbert space, least absolute deviation and group Lasso techniques. Based on the first method, the second estimator applies the pre-whitening technique and estimates the error covariance function by using functional principal component analysis. Simulation studies are conducted to examine the performance of the proposed methods in small sample sizes. The method is also applied to the Canadian weather data set, which consists of the daily average temperature and precipitation observed by 35 meteorological stations across Canada from 1960 to 1994. Numerical simulations and real data analysis show a good performance of the proposed robust methods for function-on-scalar models. [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]

In this paper, we propose a tree-based method called Multivariate RE-EM tree, which combines the regression tree and the linear mixed effects model for modeling multivariate response longitudinal or clustered data. The Multivariate RE-EM tree method estimates a population-level single tree structure that is driven by the multiple responses simultaneously and object-level random effects for each response variable, where correlation between the response variables and between the associated random effects are each allowed. Through simulation studies, we verify the advantage of the Multivariate RE-EM tree over the use of multiple univariate RE-EM trees and the Multivariate Regression Tree. We apply the Multivariate RE-EM tree to analyze a real data set that contains multidimensional nonfinancial characteristics of poverty of different countries as responses, and various potential causes of poverty as predictors. [ABSTRACT FROM AUTHOR]

Standard long memory models are in abundance in the literature today. Selecting the best such a model in terms of capturing key requisite features and trends in data becomes a challenge. This paper addresses the issue through a sequence of Monte Carlo experiments on simulated data and introduces an interval estimate on the asymptotic variance for the long-range dependence parameter of the entire family of standard long memory time series considered within the scope of the study. [ABSTRACT FROM AUTHOR]

The shared frailty models are now popular for modelling heterogeneity in survival analysis. It assumes that the same frailty is shared by all individual members within the families. Also, it is believed that all the individuals in the population are susceptible to the event of interest and will eventually experience the event. This may not always be the situation in reality. There may be a certain fraction of the population which is non-susceptible for an event and hence may not experience the event under study. Non-susceptibility is modelled by frailty models with compound frailty distribution. Further, susceptibility may be different for different families. This can be attained by randomizing the parameter of frailty distribution. This paper incorporates both the things, non-susceptibility and different susceptibility for different families by considering compound negative binomial distribution with random probability of susceptibility as frailty distribution. The inferential problem is solved in a Bayesian framework using Markov Chain Monte Carlo methods. The proposed model is then applied to a real-life data set. [ABSTRACT FROM AUTHOR]

Two-parameter exponential distributions have a widespread application in insurance, medical and industrial production. However, incomplete samples are often obtained due to experimental conditions. In this paper, a new adaptive exponentially weighted moving average control chart, called AEWMA-LR control chart, is proposed for monitoring the quality characteristics of two-parameter exponential distributions based on type-II censored data. The proposed monitoring scheme aims to achieve an adaptive effect by combining exponentially weighted moving averages and adjusting the weight factors according to the relative magnitude of the estimated location and scale parameter shifts. We explored the effects of smooth parameters, sample size, and censored parameters on the performance of AEWMA-LR control charts through a Monte Carlo simulation study. Then, a comparative analysis was conducted with existing EWMA-LR and EWMA-Max-MLE control charts based on the two-parameter exponential model. The simulation results of zero-state average run length (ARL) and conditional expected delay (CED) show that the proposed monitoring scheme outperforms the existing control charts. Finally, to demonstrate the usefulness of the AEWMA-LR control chart in real-world applications, we give three instances of two-parameter exponential distributions based on type-II right censored data. [ABSTRACT FROM AUTHOR]

This paper proves that in mixed linear model, the analysis of variance estimation (ANOVAE), the minimum norm quadratic unbiased estimation (MINQUE), the spectral decomposition estimation (SDE) and the restricted maximum likelihood estimation (RMLE) of variance components are the same under some conditions. Based on this result, we construct a linear Bayes estimation (LBE) for the parameter vector consisting of variance components and establish its superiorities. Numerical computations and an illustration show that the LBE is comparable to Lindley's approximation, Tierney and Kadane's approximation and the usual Bayes estimation (UBE) obtained by the MCMC method and easy to use as well. [ABSTRACT FROM AUTHOR]

This paper introduces a new bivariate integer-valued autoregressive of order (1) (BINAR(1)) model with negative binomial (NB) innovations under non-stationary moments. The purpose of this time series process is mainly to model series that are affected by time-dependent covariate effects and that, in particular, exhibit different levels of over-dispersion which is a phenomenon commonly noticed in many real-life series applications. In this proposed model, the cross-correlation is induced locally by allowing the current counting series observation to relate with the previous-lagged observation of the other series or vice versa while the pair of NB innovations are assumed uncorrelated. The estimation of the regression, over-dispersion and dependence parameters is conducted using a generalized quasi-likelihood (GQL) approach since the specification of the likelihood function, under non-stationarity, is rather difficult to specify in the above situation. Monte-Carlo simulation experiments are executed to assess the quality of the GQL estimators. The model is also applied and compared with other bivariate time series models to some real-life series in Mauritius. [ABSTRACT FROM AUTHOR]

Classification and feature selection play an important role in knowledge discovery in high-dimensional data. Although penalized Support Vector Machine (SVM) is among the most powerful methods for classification and automatic feature selection in high-dimensional feature space, it is not directly applicable to ultrahigh-dimensional cases, wherein the number of features far exceeds the sample size. In this paper, we suggest an efficient two-step method for simultaneous classification and identifying important features in the setting of ultrahigh-dimensional models. Specifically, we first develop an independence screening procedure to reduce the dimensionality of the feature space to a moderate scale, and then penalized support vector machine is applied to the dimension-reduced feature space to select important features further and estimate the coefficients, via a (penalized) model fit. Implementation of the suggested two-step method is not limited by the dimensionality of the models and entails much less computational cost. Numerical examples and a real data analysis are used to demonstrate the finite sample performance of our proposal. [ABSTRACT FROM AUTHOR]

We consider the problem of simultaneous variable selection and parameter estimation in an ultra-high dimensional linear regression model. The adaptive penalty functions are used in this regard to achieve the oracle variable selection property with simpler assumptions and lesser computational burden. Noting the non-robust nature of the usual adaptive procedures (e.g. adaptive LASSO) based on the squared error loss function against data contamination, quite frequent with modern large-scale data sets (e.g. noisy gene expression data, spectra and spectral data), in this paper, we present a new adaptive regularization procedure using a robust loss function based on the density power divergence (DPD) measure under a general class of error distributions. We theoretically prove that the proposed adaptive DPD-LASSO estimator of the regression coefficients is highly robust, consistent, asymptotically normal and leads to robust oracle-consistent variable selection under easily verifiable assumptions. Numerical illustrations are provided for the mostly used normal and heavy-tailed error densities. Finally, the proposal is applied to analyse an interesting spectral dataset, in the field of chemometrics, regarding the electron-probe X-ray microanalysis (EPXMA) of archaeological glass vessels from the 16th and 17th centuries. [ABSTRACT FROM AUTHOR]

This paper establishes a new estimator for simple linear measurement error models with correlated errors. Under a small-noise asymptotic regime and using perturbation theory, an unbiased estimator has been developed. The consistency and the asymptotic normality of the new estimator have been established and then validated by using synthetic data. Moreover, the confidence intervals of the slope have been revisited. Simulation results show that our estimator is certainly the most stable of existing methods and its performance exceeds that of other existing methods in terms of coverage and interval length. [ABSTRACT FROM AUTHOR]

Of interest in this paper is the development of a model that uses fixed, then inverse sampling of binary data that is subject to false-positive misclassification in an effort to estimate a proportion. From this model, both the proportion of success and false-positive misclassification rate may be estimated. Also, three first-order likelihood-based confidence intervals for the proportion of success are mathematically derived and studied via a Monte Carlo simulation. The simulation results indicate that the likelihood ratio interval is generally preferable over the Wald and score interval. Lastly, the model is applied to two different real-world medical data sets. [ABSTRACT FROM AUTHOR]

This paper firstly studies the coefficients estimation of the AR model with normal innovation by proposing an asymptotically honest generalized fiducial (AHGF) method. Furthermore, the AHGF method is introduced to skew-normal setting. Simulation results show that the AHGF method shows more advantages than traditional methods. Specifically, the AHGF method often has a smaller mean square error for point estimation. And for interval estimation, the AHGF method behaves closer to the nominal level than other methods while maintaining comparable or shorter lengths. Finally, a temperature dataset and a sunspot series are applied to illustrate the proposed AHGF methodology. [ABSTRACT FROM AUTHOR]

To overcome the computational burden of quadratic programming in kernel expectile regression (KER), iteratively reweighted least square (IRLS) technique was introduced in literature, resulting in IRLS-KER. However, for nonlinear models, IRLS-KER involves operations with matrices and vectors of the same size as the training set. Thus, as the training set becomes large, nonlinear IRLS-KER needs a long training time and large memory. To further alleviate the training cost, this paper projects the original data into a low-dimensional space via random Fourier feature. The inner product of the random Fourier features of two data points is approximately the same as the kernel function evaluated at these two data points. Hence, it is possible to use a linear model in the new low-dimensional space to approximate the original nonlinear model, and consequently, the time/memory efficient linear training algorithms could be applied. This paper applies the idea of random Fourier features to IRLS-KER, and our testing results on simulated and real-world datasets show that, the introduction of random Fourier features makes IRLS-KER achieve similar prediction accuracy as the original nonlinear version with substantially higher time efficiency. [ABSTRACT FROM AUTHOR]

This paper, based on the E-Bayesian estimation (expected Bayesian estimation), introduced the definition of E-posterior risk (expected posterior risk); we will derive the expressions of E-Bayesian estimation and their E-posterior risk for failure probability under the compound symmetric LINEX loss function, and will compare the results with the corresponding results under the square loss function. Monte Carlo simulations compared the performances of the proposed the estimation method, and compared the results on the basis of E-posterior risk. Finally, combined with the life testing data from a type of aero engine, the calculation and reliability analysis are performed, with E-Bayesian estimation and hierarchical Bayesian estimation, respectively (also using the MCMC method). When considering evaluating the E-Bayesian estimations under different loss functions, in this paper the E-posterior risk as an the evaluation standard is proposed. [ABSTRACT FROM AUTHOR]

This article considers the Bayes analysis of generalized gamma accelerated failure time model and its two components Weibull and gamma when the given observations are left truncated and right censored. In order to perform the analysis, the paper proposes the use of an improved version of the Metropolis-Hastings algorithm, namely, the Metropolis-adjusted Langevin algorithm. Besides, the paper also checks the model compatibility and compares the considered models with its components using the Bayes factor computed on the basis of a recent methodology. A numerical illustration is provided based on a simulated as well as a real dataset. The real dataset consists of individuals infected with human immunodeficiency virus who are at the risk of acquired immunodeficiency syndrome and subsequent deaths. The numerical illustration is further extended to check the effect of different therapies including the highly active antiretroviral therapy on the lifetime of individuals. [ABSTRACT FROM AUTHOR]

In this paper, we present the practical benefits of a new random forest algorithm to deal with missing values in the sample. The purpose of this work is to compare the different solutions to deal with missing values using random forests and describe the new algorithm performance as well as its algorithmic complexity. A variety of data-missing mechanisms (MCAR, MAR, MNAR) are considered and simulated. We study the quadratic errors and the bias of our algorithm and compare them to the most popular missing values random forests algorithms in the literature. In particular, we compare those techniques for both regression and prediction purposes. This work follows the paper of Gómez-Méndez and Joly [On the consistency of a random forest algorithm in the presence of missing entries. 2020. Available from: arXiv:201105433] on the consistency of this new algorithm. [ABSTRACT FROM AUTHOR]

In this paper, the sufficient and necessary conditions for the strong consistency of least squares estimators in simple linear EV regression models are proved under widely orthant dependent random errors. The results obtained in the paper improve and extend some existing ones in the literature. Simulation studies are also carried out to support the consistency of the estimators under dependence assumption and finite samples. [ABSTRACT FROM AUTHOR]

This paper focuses on the differential network analysis between two Gaussian graphical models (GGMs). We introduce a new framework for inferring the structural differences between two GGMs by adopting the elegant symmetrized data aggregation (SDA) which proceeds by sample splitting, data screening, and information aggregation to achieve the false discovery rate (FDR) control. The theoretical guarantee for the FDR control is established to verify the validity of this procedure. Simulation studies show that the proposed method delivers a reasonable FDR control with remarkable power. The method is applied to a TCGA breast cancer data set to identify the gene network rewiring between the luminal A and basal-like subtypes. [ABSTRACT FROM AUTHOR]

In the analysis of clustered or longitudinal data structures, such as those coming from surveys or trials, it is desirable to accurately estimate the dependence parameters within repeated measurements. Marginal models together with the generalized estimating equation allow to consistently estimate regression coefficients. Inference may be problematic for small and moderate sample sizes, or with models involving many covariates. Moreover, the correlation structure may be misspecified leading to a substantial bias in the sandwich covariance matrix estimator. The paper focuses on Gaussian with exchangeable correlation matrix model and proposes to use adjustments of the score function aiming at mean and median bias reduction of maximum likelihood estimates. Extensive simulation studies show a remarkable performance of the proposed methods. In addition, we show that the bias reduction methods maintain an appreciable robustness with respect to the maximum likelihood under misspecification of the correlation matrix. [ABSTRACT FROM AUTHOR]

Longitudinal data arise frequently in many economic studies and epidemiological research. In this paper, we investigate the partially linear additive model for longitudinal data in the framework of quantile regression. To incorporate the within-subject correlation, we develop an estimation procedure using quadratic inference function (QIF) and polynomial spline approximation for unknown nonparametric functions. The theoretical properties of the resulting estimators are established, where the nonparametric functions achieve the optimal convergence rate and the parametric components are asymptotically normal even when the number of parameters in the linear part is diverging. We also propose a variable selection procedure based on penalization. Since the objective function is discontinuous, a practical estimation procedure is proposed using induced smoothing and we prove that the smoothed estimator is asymptotically equivalent to the original estimator. The proposed methods are evaluated via simulation studies and a real data application. [ABSTRACT FROM AUTHOR]

High-dimensional data often display heteroscedasticity. If the heteroscedasticity is neglected in the regression model, it will produce inefficient inference for the regression coefficients. Quantile regression is not only robust to outliers, but also accommodates heteroscedasticity. This paper aims to simultaneously carry out variable selection and heteroscedasticity identification for the linear location-scale model under a unified framework. We develop a regularized multiple quantile regression approach simultaneously identifying the heteroscedasticity, seeking common features of quantile coefficients and eliminating irrelevant variables. We also establish the theoretical properties of the proposed method under some regularity conditions. Simulation studies are conducted to evaluate the finite sample performance of the proposed method, showing that it is able to identify the covariates that affect the variability of the response. We further apply the proposed method to analyse the Wage data. [ABSTRACT FROM AUTHOR]

In statistics, regression analysis is a method for predicting a target variable by establishing the optimal linear relationship between the dependent and independent variables. The ordinary least squares estimator (OLSE) is the optimal estimation method in classical regression analysis based on the Gauss–Markov theorem if the essential assumptions of normality, independence of error terms, and little or no multicollinearity in the covariates are satisfied. OLSE is profoundly affected by the collinearity between explanatory variables and outlier problems. Therefore, we require resilient strategies to resolve these challenges. Robust stochastic ridge regression is an alternative optimization problem to least squares regression when data are simultaneously contaminated by anomalies, influential observations, and multicollinearity. To combat outliers and multicollinearity problems, a robust stochastic ridge regression estimator based on the least squares trimmed method is proposed in this paper. Using simulated and real data sets, the efficacy of the proposed method with correlated and uncorrelated errors is then evaluated. [ABSTRACT FROM AUTHOR]

In this paper, statistical inferences for the parameters, reliability, and failure rate functions (as parameters) of the exponentiated Kies distribution are accomplished using maximum likelihood and both Lindley and Markov chain Monte Carlo techniques, under adaptive Type-II progressive censoring. Depending on the Fisher information matrix and the delta method, we find the approximate confidence intervals for the parameters and the reliability and failure rate functions, respectively. Furthermore, the samples generated from Markov chains Monte Carlo are used to generate credible intervals for the parameters, reliability, and failure rates functions. Symmetric and asymmetric loss functions are also used to find Bayes estimators using Markov chain Monte Carlo and Lindley techniques. Comparisons between the two techniques of evaluation for different estimators under different sizes of data sets are conducted. Finally, a real-life example is applied to clarify the results of the used techniques. [ABSTRACT FROM AUTHOR]