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Partially linear models provide a valuable tool for modeling failure time data with nonlinear covariate effects. Their applicability and importance in survival analysis have been widely acknowledged. To date, numerous inference methods for such models have been developed under traditional right censoring. However, the existing studies seldom target interval‐censored data, which provide more coarse information and frequently occur in many scientific studies involving periodical follow‐up. In this work, we propose a flexible class of partially linear transformation models to examine parametric and nonparametric covariate effects for interval‐censored outcomes. We consider the sieve maximum likelihood estimation approach that approximates the cumulative baseline hazard function and nonparametric covariate effect with the monotone splines and B$$ B $$‐splines, respectively. We develop an easy‐to‐implement expectation‐maximization algorithm coupled with three‐stage data augmentation to facilitate maximization. We establish the consistency of the proposed estimators and the asymptotic distribution of parametric components based on the empirical process techniques. Numerical results from extensive simulation studies indicate that our proposed method performs satisfactorily in finite samples. An application to a study on hypobaric decompression sickness suggests that the variable TR360 exhibits a significant dynamic and nonlinear effect on the risk of developing hypobaric decompression sickness. [ABSTRACT FROM AUTHOR]

Cointegration analysis was developed for nonstationary linear processes that exhibit stationary relationships between coordinates. Estimation of the cointegration relationships in a multidimensional cointegrated process typically proceeds in two steps. First, the rank is estimated, then the auto‐regression matrix is estimated, conditionally on the estimated rank (reduced rank regression). The asymptotics of the estimator is usually derived under the assumption of knowing the true rank. In this paper, we quantify the asymptotic bias and find the asymptotic distributions of the cointegration estimator in case of misspecified rank. Furthermore, we suggest a new class of weighted reduced rank estimators that allow for more flexibility in settings where rank selection is hard. We show empirically that a proper choice of weights can lead to increased predictive performance when there is rank uncertainty. Finally, we illustrate the estimators on empirical EEG data from a psychological experiment on visual processing. [ABSTRACT FROM AUTHOR]

We construct bootstrap confidence intervals for a monotone regression function. It has been shown that the ordinary nonparametric bootstrap, based on the nonparametric least squares estimator (LSE) f^n, is inconsistent in this situation. We show that an n2/5‐consistent bootstrap can be based on the smoothed f^n, to be called the SLSE (Smoothed Least Squares Estimator). The asymptotic pointwise distribution of the SLSE is derived. The confidence intervals, based on the smoothed bootstrap, are compared to intervals based on the (not necessarily monotone) Nadaraya Watson estimator and the effect of Studentization is investigated. We also give a method for automatic bandwidth choice, correcting work in Sen and Xu (2015). Analogous methods for constructing confidence intervals in the current status model are discussed, improving on work in Groeneboom and Hendrickx (2018). [ABSTRACT FROM AUTHOR]

In observational studies with time‐to‐event outcomes, the g‐formula can be used to estimate a treatment effect in the presence of confounding factors. However, the asymptotic distribution of the corresponding stochastic process is complicated and thus not suitable for deriving confidence intervals or time‐simultaneous confidence bands for the average treatment effect. A common remedy are resampling‐based approximations, with Efron's nonparametric bootstrap being the standard tool in practice. We investigate the large sample properties of three different resampling approaches and prove their asymptotic validity in a setting with time‐to‐event data subject to competing risks. The usage of these approaches is demonstrated by an analysis of the effect of physical activity on the risk of knee replacement among patients with advanced knee osteoarthritis. [ABSTRACT FROM AUTHOR]

We propose a modified parsimonious model averaging method under heteroscedasticity by incorporating the covariance matrix into the weight choice criterion. We demonstrate that when correctly specified models exist in the candidate model set, the weight assigned to the smallest correct model tends to 1. This leads to the consistency of variable selection and the asymptotic normality of the modified parsimonious model averaging estimator. Furthermore, we prove its asymptotic optimality within the given weight space when all candidate models are misspecified. Numerical simulations indicate that, in the presence of heteroscedasticity, the modified parsimonious model averaging estimator outperforms the unmodified version in terms of prediction accuracy. As an illustration example, we apply this method to predict housing rental prices in Fengtai District, Beijing. [ABSTRACT FROM AUTHOR]

Let X1,…,Xn$$ {\mathbf{X}}_1,\dots, {\mathbf{X}}_n $$ be a sequence of independence random vectors from Np(μ,Σ)$$ {N}_p\left(\boldsymbol{\mu}, \boldsymbol{\varSigma} \right) $$ with population correlation matrix Rn$$ {\mathbf{R}}_n $$, and its sample correlation matrix is denoted as R^n=(r^ij)p×p$$ {\hat{\mathbf{R}}}_n={\left({\hat{r}}_{ij}\right)}_{p\times p} $$, where the matrix element r^ij$$ {\hat{r}}_{ij} $$ represents the Pearson correlation coefficient between the i$$ i $$ and j$$ j $$ columns of the data matrix (X1,…,Xn)′$$ {\left({\mathbf{X}}_1,\dots, {\mathbf{X}}_n\right)}^{\prime } $$. R^n$$ {\hat{\mathbf{R}}}_n $$ is an interesting part in multivariate analysis, and the likelihood ratio test (LRT) statistic used to test the complete independence of all components of X$$ \mathbf{X} $$ can be expressed as a function of R^n$$ {\hat{\mathbf{R}}}_n $$. On this basis, under the condition that the sample size n$$ n $$ and the dimension p$$ p $$ satisfy p/n→y∈(0,1]$$ p/n\to y\in \left(0,1\right] $$ as n→∞$$ n\to \infty $$, we derive the moderate deviation principle (MDP) of the LRT statistic for the hypothesis testing problem H0:Rn=Ip$$ {H}_0:{\mathbf{R}}_n={\mathbf{I}}_p $$ vs H1:Rn≠Ip$$ {H}_1:{\mathbf{R}}_n\ne {\mathbf{I}}_p $$. [ABSTRACT FROM AUTHOR]

Differential privacy is a foundational concept for safeguarding sensitive individual information when releasing data or statistical analysis results. In this study, we concentrate on the protection of privacy in the context of goodness‐of‐fit (GOF) and independence tests, utilizing perturbed contingency tables that adhere to Gaussian differential privacy within the high‐privacy regime, where the degrees of privacy protection increase as the sample size increases. We introduce private test procedures for GOF, independence of two variables and the equality of proportions in paired samples, similar to McNemar's test. For each of these hypothesis testing situations, we propose private test statistics based on the χ2$$ {\chi}^2 $$ statistics and establish their asymptotic null distributions. We numerically confirm that Type I error rates of the proposed private test procedures are well controlled and have adequate power for larger sample sizes and effect sizes. The proposal is demonstrated in private inferences based on the American Time Use Survey data. [ABSTRACT FROM AUTHOR]

A mediation analysis approach is proposed for multiple exposures, multiple mediators, and a continuous scalar outcome under the linear structural equation modeling framework. It assumes that there exist orthogonal components that demonstrate parallel mediation mechanisms on the outcome, and thus is named principal component mediation analysis (PCMA). Likelihood‐based estimators are introduced for simultaneous estimation of the component projections and effect parameters. The asymptotic distribution of the estimators is derived for low‐dimensional data. A bootstrap procedure is introduced for inference. Simulation studies illustrate the superior performance of the proposed approach. Applied to a proteomics‐imaging dataset from the Alzheimer's disease neuroimaging initiative (ADNI), the proposed framework identifies protein deposition – brain atrophy – memory deficit mechanisms consistent with existing knowledge and suggests potential AD pathology by integrating data collected from different modalities. [ABSTRACT FROM AUTHOR]

We in this article propose a novel non‐parametric estimator for the volatility function within a broad context that encompasses nonlinear time series models as a special case. The new estimator, built on the mode value, is designed to complement existing mean volatility measures to reveal distinct data features. We demonstrate that the suggested modal volatility estimator can be obtained asymptotically as well as if the conditional mean regression function were known, assuming observations are from a strictly stationary and absolutely regular process. Under mild regularity conditions, we establish that the asymptotic distributions of the resulting estimator align with those derived from independent observations, albeit with a slower convergence rate compared to non‐parametric mean regression. The theory and practice of bandwidth selection are discussed. Moreover, we put forward a variance reduction technique for the modal volatility estimator to attain asymptotic relative efficiency while maintaining the asymptotic bias unchanged. We numerically solve the modal regression model with the use of a modified modal‐expectation‐maximization algorithm. Monte Carlo simulations are conducted to assess the finite sample performance of the developed estimation procedure. Two real data analyses are presented to further illustrate the newly proposed model in practical applications. To potentially enhance the accuracy of the bias term, we in the end discuss the extension of the method to local exponential modal estimation. We showcase that the suggested exponential modal volatility estimator shares the same asymptotic variance as the non‐parametric modal volatility estimator but may exhibit a smaller bias. [ABSTRACT FROM AUTHOR]

In the widely used predictive regression model, any possible serial correlation in innovations leads to estimation bias and statistical inference distortions. Hence, it is important to pretest the existence of such serial correlation. Nevertheless, in the presence of embedded endogeneity, which is a common problem in the predictive regression setting, traditional serial correlation tests such as Box–Pierce (BP) and Ljung–Box (LB) tests are found to perform poorly. Motivated by this, we develop a new portmanteau test in this article as a pretest for serial correlation in predictive regression under possible embedded endogeneity. This test is based on the sample splitting idea and the jackknife empirical likelihood method. The asymptotic distribution of the proposed test has been derived, and the Monte Carlo simulations confirm good finite sample performances. As an illustration, we apply our proposed test in pretesting the serial correlation in predictive regression, where financial variables are used to predict the excess return of S&P 500. [ABSTRACT FROM AUTHOR]

For stationary time series with regularly varying marginal distributions, an important problem is to estimate the associated tail index which characterizes the power‐law behavior of the tail distribution. For this, various results have been developed for independent data and certain types of dependent data. In this article, we consider the problem of tail index estimation under a recently proposed notion of serial tail dependence called the tail adversarial stability. Using the technique of adversarial innovation coupling and a martingale approximation scheme, we establish the consistency and central limit theorem of the tail index estimator for a general class of tail dependent time series. Based on the asymptotic normal distribution from the obtained central limit theorem, we further consider an application to cluster a large number of regularly varying time series based on their tail indices by using a robust mixture algorithm. The results are illustrated using numerical examples including Monte Carlo simulations and a real data analysis. [ABSTRACT FROM AUTHOR]

In recent years, significant advancements have been made in the field of identifying financial asset price bubbles, particularly through the development of time‐series unit‐root tests featuring fractionally integrated errors and panel unit‐root tests. This study introduces an innovative approach for assessing the sign of the persistence parameter (α) within a panel fractional Ornstein‐Uhlenbeck process, based on the least squares estimator of α. This method incorporates three distinct test statistics based on the Hurst parameter (H), which can take values in the range of (1/2,1), be equal to 1/2, or fall within the interval of (0,1/2). The null hypothesis corresponds to α=0. Based on a panel of continuous records of observations, the null asymptotic distributions are obtained when the time span (T) is fixed and the number of cross sections (N) goes to infinity. The power function of the tests is obtained under the local alternative where α is close to zero in the order of 1/(TN). This alternative covers the departure from the unit root hypothesis from the explosive side, enabling the calculation of lower power in bubble tests. The hypothesis testing problem and the local power function are also considered when a panel of discrete‐sampled observations is available under a sequential limit, that is, the sampling interval shrinks to zero followed by the N goes to infinity. [ABSTRACT FROM AUTHOR]

We propose a new functional additive hazards model to investigate the potential effects of functional and scalar predictors on mortality risks, and develop a penalized least squares estimation method for model parameters based on a pseudoscore estimating equation. A reproducing kernel Hilbert space approach is used to establish the consistency, convergence rate, and joint asymptotic distribution of the resulting estimators for finite‐dimensional and infinite‐dimensional parameters. Our simulation studies demonstrate that the proposed estimation procedure performs well. For illustration, we apply the proposed method to the Medical Information Mart for Intensive Care III dataset. [ABSTRACT FROM AUTHOR]

Summary: The dynamic ranking, due to its increasing importance in many applications, is becoming crucial, especially with the collection of voluminous time‐dependent data. One such application is sports statistics, where dynamic ranking aids in forecasting the performance of competitive teams, drawing on historical and current data. Despite its usefulness, predicting and inferring rankings pose challenges in environments necessitating time‐dependent modelling. This paper introduces a spectral ranker called Kernel Rank Centrality, designed to rank items based on pairwise comparisons over time. The ranker operates via kernel smoothing in the Bradley–Terry model, utilising a Markov chain model. Unlike the maximum likelihood approach, the spectral ranker is nonparametric, demands fewer model assumptions and computations and allows for real‐time ranking. We establish the asymptotic distribution of the ranker by applying an innovative group inverse technique, resulting in a uniform and precise entrywise expansion. This result allows us to devise a new inferential method for predictive inference, previously unavailable in existing approaches. Our numerical examples showcase the ranker's utility in predictive accuracy and constructing an uncertainty measure for prediction, leveraging data from the National Basketball Association (NBA). The results underscore our method's potential compared with the gold standard in sports, the Arpad Elo rating system. [ABSTRACT FROM AUTHOR]

In this article, we show a limit result for the reliability function of a system—that is, the probability that the whole system is still operational after a certain given time—when the number of components of the system grows to infinity. More specifically, we consider a sequence of mixed coherent systems whose components are homogeneous and non‐repairable, with failure‐times governed by a Lévy‐Frailty Marshall–Olkin (LFMO) distribution—a distribution that allows simultaneous component failures. We show that under integrability conditions the reliability function converges to the probability of a first‐passage time of a Lévy subordinator process. To the best of our knowledge, this is the first result to tackle the asymptotic behavior of the reliability function as the number of components of the system grows. To illustrate our approach, we give an example of a parametric family of reliability functions where the system failure time converges in distribution to an exponential random variable, and give computational experiments testing convergence. [ABSTRACT FROM AUTHOR]

In this paper, we propose a correlation‐based test for the evaluation of two competing forecasts. Under the null hypothesis of equal correlations with the target variable, we derive the asymptotic distribution of our test using the Delta method. This null hypothesis is not necessarily equivalent to the null of equal Mean Squared Prediction Errors (MSPE). Specifically, it might be the case that the forecast displaying the lowest MSPE also exhibits the lowest correlation with the target variable: this is known as "The MSPE paradox." In this sense, our approach should be seen as complementary to traditional tests of equality in MSPE. Monte Carlo simulations indicate that our test has good size and power. Finally, we illustrate the use of our test in an empirical exercise in which we compare two different inflation forecasts for a sample of OECD economies. We find more rejections of the null of equal correlations than rejections of the null of equality in MSPE. [ABSTRACT FROM AUTHOR]

Using ‘working’ assumptions on conditional third and fourth moments of errors, we propose a method of moments estimator that can have improved efficiency over the popular Gaussian quasi‐maximum likelihood estimator (GQMLE). Higher‐order moment assumptions are not needed for consistency – we only require the first two conditional moments to be correctly specified – but the optimal instruments are derived under these assumptions. The working assumptions allow both asymmetry in the distribution of the standardized errors as well as fourth moments that can be smaller or larger than that of the Gaussian distribution. The approach is related to the generalized estimation equations (GEE) approach – which seeks the improvement of estimators of the conditional mean parameters by making working assumptions on the conditional second moments. We derive the asymptotic distribution of the new estimator and show that it does not depend on the estimators of the third and fourth moments. A simulation study shows that the efficiency gains over the GQMLE can be non‐trivial. [ABSTRACT FROM AUTHOR]

This paper analyzes several covariance matrix U‐tests, which are constructed by modifying the classical John‐Nagao and Ledoit‐Wolf tests, under the elliptically distributed data structure. We study the limiting distributions of these location‐invariant test statistics as the data dimension p$$ p $$ may go to infinity in an arbitrary way as the sample size n$$ n $$ does. We find that they tend to have unsatisfactory size performances for general elliptical population. This is mainly because such population often possesses high‐order correlations among their coordinates. Taking such kind of dependency into consideration, we propose necessary corrections for these tests to cope with elliptically high‐dimensional data. For computational efficiency, alternative forms of the new test statistics are also provided. We derive the universal (n,p)$$ \left(n,p\right) $$ asymptotic null distributions of the proposed test statistics under elliptical distributions and beyond. The powers of the proposed tests are further investigated. The accuracy of the tests is demonstrated by simulations and an empirical study. [ABSTRACT FROM AUTHOR]

The win ratio has in the recent decade gained popularity for analyzing prioritized multiple event data in clinical cohort studies, in particular within cardiovascular research. The literature on estimation of the win ratio using censored event data is however sparse. The methods that have been suggested have either an insufficient adjustment of the censoring or by assuming the the win and loss probabilities are proportional over time. The assumption of proportional win and loss probabilities will often in practice not be satisfied. In this paper, we present estimates for the win ratio, and win and loss probabilities, under independent right‐censoring and derive the asymptotic distribution of the estimates. The proposed win ratio estimate does not require the assumption of proportional win and loss probabilities. The small sample properties of the proposed method are studied in a simulation study showing that the variance formula is accurate even for small samples. The method is applied on two data sets. [ABSTRACT FROM AUTHOR]

Many financial time series not only have varying structures at different quantile levels and exhibit the phenomenon of conditional heteroscedasticity at the same time but also arrive in the stream. Quantile double‐autoregression is very useful for time series analysis but faces challenges with model fitting of streaming data sets when estimating other quantiles in subsequent batches. This article proposes a renewable estimation method for quantile double‐autoregression analysis of streaming time series data due to its ability to break with storage barrier and computational barrier. Moreover, the proposed flexible parametric structure of the quantile function enables us to predict any interested quantile value without quantile curve crossing problem or keeping the desirable monotone property of the conditional quantile function. The proposed methods are illustrated using current data and the summary statistics of historical data. Theoretically, the proposed statistic is shown to have the same asymptotic distribution as the standard version computed on an entire data stream with the data batches pooled into one data set, without additional condition. Simulation studies and an empirical example are presented to illustrate the finite sample performance of the proposed methods. [ABSTRACT FROM AUTHOR]

We suggest novel correlation coefficients which equal the maximum correlation for a class of bivariate Lancaster distributions while being only slightly smaller than maximum correlation for a variety of further bivariate distributions. In contrast to maximum correlation, however, our correlation coefficients allow for rank and moment‐based estimators which are simple to compute and have tractable asymptotic distributions. Confidence intervals resulting from these asymptotic approximations and the covariance bootstrap show good finite‐sample coverage. In a simulation, the power of asymptotic as well as permutation tests for independence based on our correlation measures compares favorably with competing methods based on distance correlation or rank coefficients for functional dependence, among others. Moreover, for the bivariate normal distribution, our correlation coefficients equal the absolute value of the Pearson correlation, an attractive feature for practitioners which is not shared by various competitors. We illustrate the practical usefulness of our methods in applications to two real data sets. [ABSTRACT FROM AUTHOR]

Inverse Weibull, lognormal, and inverse Gaussian are some commonly used statistical distributions for modeling positively skewed failure lifetime data. These distributions share some interesting properties among themselves like they all have uni‐modal hazard rates. In this paper, we address the problem of discriminating among these statistical distributions to consider a more appropriate lifetime model. We first consider the complete samples and make use of the maximized log‐likelihood approach for choosing the correct model. We also obtain the expressions for logarithmic of defined test statistics, and associated asymptotic distributions. We then extend our discussion based on the observed sample in the presence of some censoring. We perform a simulation study in both cases to compare the probabilities of correct selection. Furthermore, for a given probability of correct selection and user‐specified protection level, we present a discussion to determine the minimum sample size required to discriminate among the three lifetime models. Finally, two real data sets are analyzed to illustrate the proposed methodology. In our findings, we observed that model parameters and methods of estimating unknown parameters play very important roles in the discrimination process, and sample size and the proportion of censoring become key factors to ensure a high probability of selecting a correct model. [ABSTRACT FROM AUTHOR]

Existing methods for fitting spatial autoregressive models have various strengths and weaknesses. For example, the maximum likelihood estimation (MLE) approach yields efficient estimates but is computationally burdensome. Computationally efficient methods, such as generalized method of moments (GMMs) and spatial two‐stage least squares (2SLS), typically require exogenous covariates to be significant, a restrictive assumption that may fail in practice. We propose a new estimating equation approach, termed combined moment equation (COME), which combines the first moment with covariance conditions on the residual terms. The proposed estimator is less computationally demanding than MLE and does not need the restrictive exogenous conditions as required by GMM and 2SLS. We show that the proposed estimator is consistent and establish its asymptotic distribution. Extensive simulations demonstrate that the proposed method outperforms the competitors in terms of bias, efficiency, and computation. We apply the proposed method to analyze an air pollution study, and obtain some interesting results about the spatial distribution of PM2.5 concentrations in Beijing. [ABSTRACT FROM AUTHOR]

Summary: Data related to the counting of elements of variable character are frequently encountered in time series studies. This paper brings forward a new class of k$$ k $$th‐order dependence‐driven random coefficient mixed thinning integer‐valued autoregressive time series model (DDRCMTINAR(k$$ k $$)) to deal with such data. Stationarity and ergodicity properties of the proposed model are derived in detail. The unknown parameters are estimated by conditional least squares, and modified quasi‐likelihood and asymptotic normality of the obtained parameter estimators is established. The performances of the adopted estimate methods are checked via simulations, which present that modified quasi‐likelihood estimators perform better than the conditional least squares considering the proportion of within‐Ω$$ \Omega $$ estimates in certain regions of the parameter space. The validity and practical utility of the model are investigated by epileptic seizure data and COVID‐19 data of suspected cases in China. [ABSTRACT FROM AUTHOR]

Summary: We propose a flexible stochastic production frontier model with fixed effects for the panel data in which the semiparametric frontier is additive with bivariate interactions. To avoid potential misspecification and/or "wrong skew problem" due to distributional assumptions, we model the conditional mean of the inefficiency to depend on environmental variables and to be known up to a vector of parameters. We propose a difference‐based estimator for parameters characterizing the conditional mean of the inefficiency term, a profile series estimator, and a kernel‐based one‐step backfitting estimator for the frontier to facilitate inference. We establish their asymptotic properties and show that each component in the frontier estimated by the kernel‐based backfitting has the same asymptotic distribution as the one estimated with the true knowledge on the other components in the frontier (i.e., the oracle property). Through a Monte Carlo study, we demonstrate that the proposed estimators perform well in finite samples. Utilizing a panel of Chinese firm‐level data in 2000–2006, we apply our method to estimate the frontier and efficiency scores and conclude that export plays a significant role in reducing the efficiency of firms. [ABSTRACT FROM AUTHOR]

In this article, we develop additive autoregressive models (Add‐ARM) for the time series data with matrix valued predictors. The proposed models assume separable row, column and lag effects of the matrix variables, attaining stronger interpretability when compared with existing bilinear matrix autoregressive models. We utilize the Gershgorin's circle theorem to impose some certain conditions on the parameter matrices, which make the underlying process strictly stationary. We also introduce the alternating least squares estimation method to solve the involved equality constrained optimization problems. Asymptotic distributions of the parameter estimators are derived. In addition, we employ hypothesis tests to run diagnostics on the parameter matrices. The performance of the proposed models and methods is further demonstrated through simulations and real data analysis. [ABSTRACT FROM AUTHOR]

Missing data in covariates can result in biased estimates and loss of power to detect associations. We consider Cox regression in which some covariates are subject to missing. The inverse probability weighted approach is often applied to regression analysis with missing covariates. Inverse probability weighted estimators typically are less efficient than likelihood‐based estimators, but in general are more robust against model misspecification. In this article, we propose a robust best linear weighted estimator for Cox regression with missing covariates. Our proposed estimator is the projection of the simple inverse probability weighted estimator onto the orthogonal complement of the score space based on a working regression model of the observed data. The efficiency gain is from the use of the association between the survival outcome variable and the available covariates, which is the working regression model. The asymptotic distribution is derived, and the finite sample performance of the proposed estimator is examined via extensive simulation studies. The methods are applied to a colorectal cancer study to assess the association of the microsatellite instability status with colorectal cancer‐specific mortality. [ABSTRACT FROM AUTHOR]

This paper proposes a frequentist model averaging approach in the presence of parameter instability and heteroskedasticity. We derive optimal weights combining the stable and break specifications of a predictive model, with the weights from minimizing the leave‐one‐out cross‐validation information criterion (CV). We characterize the asymptotic distribution of the CV and provide the analytical expressions of the feasible optimal CV weights. Our simulations and applications forecasting the US and Taiwanese GDP growth demonstrate the superior performance of the CV model averaging relative to other methods such as the Mallows averaging, the approximate Bayesian averaging, and equal weighting. [ABSTRACT FROM AUTHOR]

Under stationary α‐mixing dependent samples, we in this article develop a novel nonlinear regression based on mode value for time series sequences to achieve robustness without sacrificing estimation efficiency. The estimation process is built on a kernel‐based objective function with a constant bandwidth (tuning parameter) that is independent of sample size and can be adjusted to maximize efficiency. The asymptotic distribution of the resultant estimator is established under suitable conditions, and the convergence rate is demonstrated to be the same as that in nonlinear mean regression. To numerically estimate the kernel mode‐based regression, we develop a modified modal‐expectation‐maximization algorithm in conjunction with Taylor expansion. A robust Wald‐type test statistic derived from the resulting estimator is also provided, along with its asymptotic distribution for the null and alternative hypotheses. The local robustness of the proposed estimation procedure is studied using influence function analysis, and the good finite sample performance of the newly suggested model is verified through Monte Carlo simulations. We finally combine the recommended kernel mode‐based regression with neural networks to develop a kernel mode‐based neural networks model, the performance of which is evidenced by an empirical examination of exchange rate prediction. [ABSTRACT FROM AUTHOR]

In this article, we derive the asymptotic distributions of residual and normalized residual empirical autocovariances and autocorrelations of (parsimonious) periodic autoregressive moving‐average (PARMA) models under the assumption that the errors are uncorrelated but not necessarily independent. We then deduce the modified portmanteau statistics. We establish the asymptotic behavior of the proposed statistics. It is shown that the asymptotic distribution of the modified portmanteau tests is that of a weighted sum of independent chi‐squared random variables, which can be different from the usual chi‐squared approximation used under independent and identically distributed assumption on the noise. We also propose another test based on a self‐normalization approach to check the adequacy of PARMA models. A set of Monte Carlo experiments and an application to financial data are presented. [ABSTRACT FROM AUTHOR]

This paper introduces a Nearly Unstable INteger‐valued AutoRegressive Conditional Heteroscedastic (NU‐INARCH) process for dealing with count time series data. It is proved that a proper normalization of the NU‐INARCH process weakly converges to a Cox–Ingersoll–Ross diffusion in the Skorohod topology. The asymptotic distribution of the conditional least squares estimator of the correlation parameter is established as a functional of certain stochastic integrals. Numerical experiments based on Monte Carlo simulations are provided to verify the behavior of the asymptotic distribution under finite samples. These simulations reveal that the nearly unstable approach provides satisfactory and better results than those based on the stationarity assumption even when the true process is not that close to nonstationarity. A unit root test is proposed and its Type‐I error and power are examined via Monte Carlo simulations. As an illustration, the proposed methodology is applied to the daily number of deaths due to COVID‐19 in the United Kingdom. [ABSTRACT FROM AUTHOR]

To tackle massive data, subsampling is a practical approach to select the more informative data points. However, when responses are expensive to measure, developing efficient subsampling schemes is challenging, and an optimal sampling approach under measurement constraints was developed to meet this challenge. This method uses the inverses of optimal sampling probabilities to reweight the objective function, which assigns smaller weights to the more important data points. Thus, the estimation efficiency of the resulting estimator can be improved. In this paper, we propose an unweighted estimating procedure based on optimal subsamples to obtain a more efficient estimator. We obtain the unconditional asymptotic distribution of the estimator via martingale techniques without conditioning on the pilot estimate, which has been less investigated in the existing subsampling literature. Both asymptotic results and numerical results show that the unweighted estimator is more efficient in parameter estimation. [ABSTRACT FROM AUTHOR]

Focusing on polygenic signal detection in high‐dimensional genetic association studies of complex traits, we develop a stable and adaptive test for generalized linear models to accommodate different alternatives. To facilitate valid post‐selection inference for high‐dimensional data, our study here adheres to the original sample‐splitting principle but does so repeatedly to increase stability of the inference. We show the asymptotic null distribution of the proposed test for both fixed and diverging numbers of variants. We also show the asymptotic properties of the proposed test under local alternatives, providing insights on why power gain attributed to variable selection and weighting can compensate for efficiency loss due to sample splitting. We support our analytical findings through extensive simulation studies and two applications. The proposed procedure is computationally efficient and has been implemented as the R package DoubleCauchy. [ABSTRACT FROM AUTHOR]

We develop a group of robust, nonparametric hypothesis tests that detect differences between the covariance operators of several populations of functional data. These tests, called functional Kruskal–Wallis tests for covariance, or FKWC tests, are based on functional data depth ranks. FKWC tests work well even when the data are heavy‐tailed, which is shown both in simulation and theory. FKWC tests offer several other benefits: they have a simple asymptotic distribution under the null hypothesis, they are computationally cheap, and they possess transformation‐invariance properties. We show that under general alternative hypotheses, these tests are consistent under mild, nonparametric assumptions. As a result, we introduce a new functional depth function called L2‐root depth that works well for the purposes of detecting differences in magnitude between covariance kernels. We present an analysis of the FKWC test based on L2‐root depth under local alternatives. Through simulations, when the true covariance kernels have an infinite number of positive eigenvalues, we show that these tests have higher power than their competitors while maintaining their nominal size. We also provide a method for computing sample size and performing multiple comparisons. [ABSTRACT FROM AUTHOR]

In a one‐component partial least squares fit of a linear regression model, we find the asymptotic normal distribution, as the sample size and number of predictors approach infinity, of a user‐selected univariate linear combination of the coefficient estimator and give corresponding asymptotic confidence and prediction intervals. Simulation studies and an analysis of a dopamine dataset are used to support our theoretical asymptotic results and their practical application. [ABSTRACT FROM AUTHOR]

The maximum‐likelihood estimator of nonlinear panel data models with fixed effects is asymptotically biased under rectangular‐array asymptotics. The literature has devoted substantial effort to devising methods that correct for this bias as a means to salvage standard inferential procedures. The chief purpose of this paper is to show that the (recursive, parametric) bootstrap replicates the asymptotic distribution of the (uncorrected) maximum‐likelihood estimator and of the likelihood‐ratio statistic. This justifies the use of confidence sets and decision rules for hypothesis testing constructed via conventional bootstrap methods. No modification for the presence of bias needs to be made. [ABSTRACT FROM AUTHOR]

We in this paper propose a new approach for estimating conditional mode non‐parametrically to capture the 'most likely' effect built on local linear approximation, in which a parametric pilot modal regression is locally adjusted through a kernel smoothing fit to potentially reduce the bias asymptotically without affecting the variance of the estimator. Specifically, we first estimate a parametric modal regression utilizing prior information from initial studies or economic analysis, and then estimate the non‐parametric modal function based on the additive correction by eliminating the parametric feature. We derive the asymptotic normal distribution of the proposed modal estimator for both fixed and estimated parametric feature cases, and demonstrate that there is substantial room for bias reduction under certain regularity conditions. We numerically estimate the suggested modal regression model with the use of a modified modal‐expectation‐maximization (MEM) algorithm. Monte Carlo simulations and one empirical analysis are presented to illustrate the finite sample performance of the developed modal estimator. Several extensions, including multiplicative correction, generalized guidance, modal‐based robust regression and the incorporation of categorical covariates, are also discussed for the sake of completeness. [ABSTRACT FROM AUTHOR]

Human microbiome research has gained increasing importance due to its critical roles in comprehending human health and disease. Within the realm of microbiome research, the data generated often involves operational taxonomic unit counts, which can frequently present challenges such as over‐dispersion and zero‐inflation. To address dispersion‐related concerns, the generalized Poisson model offers a flexible solution, effectively handling data characterized by over‐dispersion, equi‐dispersion, and under‐dispersion. Furthermore, the realm of zero‐inflated generalized Poisson models provides a strategic avenue to simultaneously tackle both over‐dispersion and zero‐inflation. The phenomenon of zero‐inflation frequently stems from the heterogeneous nature of study populations. It emerges when specific microbial taxa fail to thrive in the microbial community of certain subjects, consequently resulting in a consistent count of zeros for these individuals. This subset of subjects represents a latent class, where their zeros originate from the genuine absence of the microbial taxa. In this paper, we introduce a novel testing methodology designed to uncover such latent classes within generalized Poisson regression models. We establish a closed‐form test statistic and deduce its asymptotic distribution based on estimating equations. To assess its efficacy, we conduct an extensive array of simulation studies, and further apply the test to detect latent classes in human gut microbiome data from the Bogalusa Heart Study. [ABSTRACT FROM AUTHOR]

The delta method for deriving asymptotic distributions is presented. Assume interest lies in fθ0 where θ0 is an unknown parameter and f is a known function. The delta method allows to immediately obtain an approximation of the distribution of the plug‐in estimator fθ̂n through the asymptotic distribution of anfθ̂n−fθ0whenever the asymptotic distribution of anθ̂n−θ0 is known and f is differentiable at θ0. This article is categorized under:Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data [ABSTRACT FROM AUTHOR]

Several procedures have been recently proposed to test the simplifying assumption for conditional copulas. Instead of considering pointwise conditioning events, we study the constancy of the conditional dependence structure when some covariates belong to general Borel conditioning subsets. We introduce several test statistics based on the equality of conditional Kendall's taus and derive their asymptotic distributions under the null hypothesis. In settings where such conditioning events are not fixed ex ante, we propose a data‐driven procedure to recursively build such relevant subsets. This procedure is based on decision trees that maximize the differences between the conditional Kendall's taus, which correspond to the leaves of the trees. Empirical results for such tests are illustrated in the Supplementary Material. Moreover, a study of the conditional dependence between financial stock returns is presented and highlights specific contagion effects of past returns. The last application deals with conditional dependence between coverage amounts in an insurance dataset. [ABSTRACT FROM AUTHOR]

The U‐statistic has been an important part of the arsenal of statistical tools. Meanwhile, the computation of it could easily become expensive. As a remedy, the idea of incomplete U‐statistics has been adopted in practice, where only a small fraction of combinations of units are evaluated. Recently, researchers proposed a new type of incomplete U‐statistics called ICUDO, which needs substantially less time of computing than all existing methods. This paper aims to study the asymptotic distributions of ICUDO to facilitate the corresponding statistical inference. This is a non‐trivial task due to the restricted randomization in the sampling scheme of ICUDO. The bootstrap approach for the finite sample distribution of ICUDO is also discussed. Lastly, we observe some intrinsic connections between U‐statistics and computer experiments in the context of integration approximation. This allows us to generalize some existing theoretical results in the latter topic. [ABSTRACT FROM AUTHOR]

Composite quantile regression (CQR) is an efficient method to estimate parameters of the linear model with non‐Gaussian random noise. The non‐smoothness of CQR loss prevents many efficient algorithms from being used. In this paper, we propose the composite smoothed quantile regression (CSQR) model and investigate the inference problem for a large‐scale dataset, in which the dimensionality p$$ p $$ is allowed to increase with the sample size n$$ n $$ while p/n∈(0,1)$$ p/n\in \left(0,1\right) $$. After applying the convolution smoothing technique to the composite quantile loss, we obtain the convex and twice differentiable CSQR loss function, which can be optimized via the gradient descent algorithm. Theoretically, we establish the non‐asymptotic error bound for the CSQR estimators and further provide the Bahadur representation and the Berry–Esseen bound, from which the asymptotic normality of CSQR estimator can be immediately derived. To make valid inference, we construct the confidence intervals that based on the asymptotic distribution. Besides, we also explore the asymptotic relative efficiency of the CSQR estimator with respect to the standard CQR estimator. At last, we provide extensive numerical experiments on both simulated and real data to demonstrate the good performance of our CSQR estimator compared with some baselines. [ABSTRACT FROM AUTHOR]

Summary: Two‐way layouts are common in grain industry research where it is often the case that there are one or more covariates. It is widely recognised that when estimating fixed effect parameters, one should also examine for possible extra error variance structure. An exact test for heteroscedasticity, when there is a covariate, is illustrated for a data set from frost trials in Western Australia. While the general algebra for the test is known, albeit in past literature, there are computational aspects of implementing the test for the two way when there are covariates. In this scenario the test is shown to have greater power than the industry standard, and because of its exact size, is preferable to use of the restricted maximum likelihood ratio test (REMLRT) based on the approximate asymptotic distribution in this instance. Formulation of the exact test considered here involves creation of appropriate contrasts in the experimental design. This is illustrated using specific choices of observations corresponding to an index set in the linear model for the two‐way layout. Also an algorithm supplied complements the test. Comparisons of size and power then ensue. The test has natural extensions when there are unbalanced data, and more than one covariate may be present. Results can be extended to Balanced Incomplete Block Designs. [ABSTRACT FROM AUTHOR]

In this paper we provide a general two‐step framework for linear projection estimators of impulse responses in structural vector autoregressions (SVARs). This framework is particularly useful for situations when structural shocks are identified from information outside the VAR (e.g. narrative shocks). We provide asymptotic results for statistical inference and discuss situations when standard inference is valid without adjustment for generated regressors, autocorrelated errors or non‐stationary variables. We illustrate how various popular SVAR models fit into our framework. Furthermore, we provide a local projection framework for invertible SVAR models that are estimated by instrumental variables (IV). This class of models results in a set of quadratic moment conditions used to obtain the asymptotic distribution of the estimator. Moreover, we analyse generalized least squares (GLS) versions of the projections to improve the efficiency of the projection estimators. We also compare the finite sample properties of various estimators in simulations. Two highlights of the Monte Carlo results are (i) for invertible VARs our two‐step IV projection estimator is more efficient compared to existing projection estimators and (ii) using the GLS projection variant with residual augmentation leads to substantial efficiency gains relative to standard OLS/IV projection estimators. [ABSTRACT FROM AUTHOR]

We propose a new class of goodness‐of‐fit tests for the logistic distribution based on a characterization related to the density approach in the context of Stein's method. This characterization‐based test is a first of its kind for the logistic distribution. The asymptotic null distribution of the test statistic is derived and it is shown that the test is consistent against fixed alternatives. The finite sample power performance of the newly proposed class of tests is compared to various existing tests by means of a Monte Carlo study. It is found that this new class of tests are especially powerful when the alternative distributions are heavy tailed, like Student's t and Cauchy, or for skew alternatives such as the log‐normal, gamma and chi‐square distributions. [ABSTRACT FROM AUTHOR]

The asymptotic distributions of the recursive out-of-sample forecast accuracy test statistics depend on stochastic integrals of Brownian motion when the models under comparison are nested. This often complicates their implementation in practice because the computation of their asymptotic critical values is burdensome. Hansen and Timmermann (2015, Econometrica) propose a Wald approximation of the commonly used recursive F-statistic and provide a simple characterization of the exact density of its asymptotic distribution. However, this characterization holds only when the larger model has one extra predictor or the forecast errors are homoscedastic. No such closed-form characterization is readily available when the nesting involves more than one predictor and heteroscedasticity or serial correlation is present. We first show through Monte Carlo experiments that both the recursive F-test and its Wald approximation have poor finite-sample properties, especially when the forecast horizon is greater than one and forecast errors exhibit serial correlation. We then propose a hybrid bootstrap method consisting of a moving block bootstrap and a residual-based bootstrap for both statistics and establish its validity. Simulations show that the hybrid bootstrap has good finite-sample performance, even in multi-step ahead forecasts with more than one predictor, and with heteroscedastic or autocorrelated forecast errors. The bootstrap method is illustrated on forecasting core inflation and GDP growth. [ABSTRACT FROM AUTHOR]

The change‐plane Cox model is a popular tool for the subgroup analysis of survival data. Despite the rich literature on this model, there has been limited investigation into the asymptotic properties of the estimators of the finite‐dimensional parameter. Particularly, the convergence rate, not to mention the asymptotic distribution, has not been fully characterized for the general model where classification is based on multiple covariates. To bridge this theoretical gap, this study proposes a maximum smoothed partial likelihood estimator and establishes the following asymptotic properties. First, it shows that the convergence rate for the classification parameter can be arbitrarily close to n−1$$ {n}^{-1} $$ up to a logarithmic factor under a certain condition on covariates and the choice of tuning parameter. Given this convergence rate result, it also establishes the asymptotic normality for the regression parameter. [ABSTRACT FROM AUTHOR]

We introduce a new family of multiple orthogonal polynomials satisfying orthogonality conditions with respect to two weights (w1,w2)$(w_1,w_2)$ on the positive real line, with w1(x)=xαe−x$w_1(x)=x^\alpha e^{-x}$ the gamma density and w2(x)=xαEν+1(x)$w_2(x) = x^\alpha E_{\nu +1}(x)$ a density related to the exponential integral Eν+1$E_{\nu +1}$. We give explicit formulas for the type I functions and type II polynomials, their Mellin transform, Rodrigues formulas, hypergeometric series, and recurrence relations. We determine the asymptotic distribution of the (scaled) zeros of the type II multiple orthogonal polynomials and make a connection to random matrix theory. Finally, we also consider two related families of mixed‐type multiple orthogonal polynomials. [ABSTRACT FROM AUTHOR]

In this study, the asymptotic distributions of the likelihood ratio test (LRT), the restricted likelihood ratio test (RLRT), the F and the sequence kernel association test (SKAT) statistics for testing an additive effect of the expected familial relatedness (FR) in a linear mixed model are examined based on an eigenvalue approach. First, the covariance structure for modeling the FR effect in a LMM is presented. Then, the multiplicity of eigenvalues for the log‐likelihood and restricted log‐likelihood is established under a replicate family setting and extended to a more general replicate family setting (GRFS) as well. After that, the asymptotic null distributions of LRT, RLRT, F and SKAT statistics under GRFS are derived. The asymptotic null distribution of SKAT for testing genetic rare variants is also constructed. In addition, a simple formula for sample size calculation is provided based on the restricted maximum likelihood estimate of the effect size for the expected FR. Finally, a power comparison of these test statistics on hypothesis test of the expected FR effect is made via simulation. The four test statistics are also applied to a data set from the UK Biobank. [ABSTRACT FROM AUTHOR]