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This paper deals with a Skorokhod's integral‐based least squares‐ (LS) type estimator of the drift parameter computed from multiple (possibly dependent) copies of the solution of a stochastic differential equation (SDE) driven by a fractional Brownian motion of Hurst index H∈(1/3,1)$$ H\in \left(1/3,1\right) $$. On the one hand, some convergence results are established on our LS estimator when H=1/2$$ H=1/2 $$. On the other hand, when H≠1/2$$ H\ne 1/2 $$, Skorokhod's integral‐based estimators cannot be computed from data, but in this paper some convergence results are established on a computable approximation of our LS estimator. [ABSTRACT FROM AUTHOR]

This paper studies generative adversarial networks (GANs) from the perspective of statistical inference. A GAN is a popular machine learning method in which the parameters of two neural networks, a generator and a discriminator, are estimated to solve a particular minimax problem. This minimax problem typically has a multitude of solutions and the focus of this paper are the statistical properties of these solutions. We address two key statistical issues for the generator and discriminator network parameters, consistent estimation and confidence sets. We first show that the set of solutions to the sample GAN problem is a (Hausdorff) consistent estimator of the set of solutions to the corresponding population GAN problem. We then devise a computationally intensive procedure to form confidence sets and show that these sets contain the population GAN solutions with the desired coverage probability. Small numerical experiments and a Monte Carlo study illustrate our results and verify our theoretical findings. We also show that our results apply in general minimax problems that may be nonconvex, nonconcave, and have multiple solutions. [ABSTRACT FROM AUTHOR]

This paper studies the autoregressive and moving average (ARMA) model with time‐functional variance (TFV) noises, called the ARMA‐TFV model. We first establish the consistency and asymptotic normality of its least squares estimator (LSE). The Wald tests and portmanteau tests are constructed based on the theory for variable selection and model checking. A simulation study is carried out to assess the performance of our approach in finite samples, and two real examples are given. It should be mentioned that the process generated from the ARMA‐TFV model is not stationary, and the technique in this paper is nonstandard and may provide insights for future research in this area. [ABSTRACT FROM AUTHOR]

Considering two-sided HT ht -values would not solve the problem, any departure of the goodness-of-fit test statistics from its median would be then interpreted as negative evidence of some level. As Sander Greenland points out, these should not be confused with the HT ht -values of realized goodness of-fit-test statistics. [Extracted from the article]

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]

Hyperspherical kernel density estimators (KDE), which use a parametric distribution as a guide, are studied in this paper. The main benefit is that these estimators improve the bias of nonguided kernel density estimators when the parametric guiding distribution is not too far from the true density, while preserving the variance. When using a von Mises‐Fisher density as guide, the proposal performs as well as the classical KDE, even when the guiding model is incorrect, and far from the true distribution. This benefit is particular for the hyperspherical setting given its compact support, and is in contrast to similar methods for real valued data. Moreover, we deal with the important issue of data‐driven selection of the smoothing parameter. Simulations and real data examples illustrate the finite‐sample performance of the proposed method, also in comparison with other recently proposed estimation methods. [ABSTRACT FROM AUTHOR]

The multivariate coefficient of variation (MCV) is an attractive and easy‐to‐interpret effect size for the dispersion in multivariate data. Recently, the first inference methods for the MCV were proposed for general factorial designs. However, the inference methods are primarily derived for one special MCV variant while there are several reasonable proposals. Moreover, when rejecting a global null hypothesis, a more in‐depth analysis is of interest to find the significant contrasts of MCV. This paper concerns extending the nonparametric permutation procedure to the other MCV variants and a max‐type test for post hoc analysis. To improve the small sample performance of the latter, we suggest a novel bootstrap strategy and prove its asymptotic validity. The actual performance of all proposed tests is compared in an extensive simulation study and illustrated by real data analysis. All methods are implemented in the R package GFDmcv, available on CRAN. [ABSTRACT FROM AUTHOR]

In this paper we study two important representations for extreme value distributions and their max‐domains of attraction (MDA), namely von Mises representation (vMR) and variation representation (VR), which are convenient ways to gain limit results. Both VR and vMR are defined via so‐called auxiliary functions ψ. Up to now, however, the set of valid auxiliary functions for vMR has neither been characterized completely nor separated from those for VR. We contribute to the current literature by introducing "universal" auxiliary functions which are valid for both VR and vMR representations for the entire MDA distribution families. Then we identify exactly the sets of valid auxiliary functions for both VR and vMR. Moreover, we propose a method for finding appropriate auxiliary functions with analytically simple structure and provide them for several important distributions. [ABSTRACT FROM AUTHOR]

Many matrix‐valued functions of an m×m Wishart matrix W, Fk(W), say, are homogeneous of degree k in W, and are equivariant under the conjugate action of the orthogonal group 풪(m), that is, Fk(HWHT)=HFk(W)HT, H∈풪(m). It is easy to see that the expectation of such a function is itself homogeneous of degree k in ∑, the covariance matrix, and are also equivariant under the action of 풪(m) on ∑. The space of such homogeneous, equivariant, matrix‐valued functions is spanned by elements of the type Wrpλ(W), where r∈{0,...,k} and, for each r, λ varies over the partitions of k−r, and pλ(W) denotes the power‐sum symmetric function indexed by λ. In the analogous case where W is replaced by W−1, these elements are replaced by W−rpλ(W−1). In this paper, we derive recurrence relations and analytical expressions for the expectations of such functions. Our results provide highly efficient methods for the computation of all such moments. [ABSTRACT FROM AUTHOR]

In this paper, we construct an approximation to the Pitman–Yor process by truncating its two‐parameter Poisson–Dirichlet representation. The truncation is based on a decreasing sequence of random weights, thus having a lower approximation error compared to the popular truncated stick‐breaking process. We develop an exact simulation algorithm to sample from the approximation process and provide an alternative MCMC algorithm for the parameter regime where the exact simulation algorithm becomes slow. The effectiveness of the simulation algorithms is demonstrated by the estimation of the functionals of a Pitman–Yor process. Then we adapt the approximation process into a Pitman–Yor process mixture model and devise a blocked Gibbs sampler for posterior inference. [ABSTRACT FROM AUTHOR]

In this paper, we modify the Bayes risk for the expectile, the so‐called variantile risk measure, to better capture extreme risks. The modified risk measure is called the adjusted standard‐deviatile. First, we derive the asymptotic expansions of the adjusted standard‐deviatile. Next, based on the first‐order asymptotic expansion, we propose two efficient estimation methods for the adjusted standard‐deviatile at intermediate and extreme levels. By using techniques from extreme value theory, the asymptotic normality is proved for both estimators for independent and identically distributed observations and for β‐mixing time series, respectively. Simulations and real data applications are conducted to examine the performance of the proposed estimators. [ABSTRACT FROM AUTHOR]

This paper studies density estimation and regression analysis with data observed on a general unit hypersphere and contaminated by measurement errors. We establish novel density and regression estimators, and study their asymptotic properties such as the rates of convergence and asymptotic normality. We also provide two types of asymptotic confidence intervals for both density and regression functions. One type is based on the asymptotic normality of their estimators and the other type is based on the empirical likelihood technique. We present practical details on the implementation of our method as well as simulation studies and real data analysis. [ABSTRACT FROM AUTHOR]

Through exploiting information from the source data to improve the fit performance on the target data, transfer learning estimations for high‐dimensional linear regression models have drawn much attention recently, but few studies focus on statistical inference and robust learning in the presence of heavy‐tailed/asymmetric errors. Using adaptive Huber regression (AHR) to achieve the bias and robustness tradeoff, in this paper we propose a robust transfer learning algorithm with high‐dimensional covariates, then construct valid confidence intervals and hypothesis tests based on the debiased lasso approach. When the transferable sources are known, a two‐step ℓ1$$ {\ell}_1 $$‐penalized transfer AHR estimator is firstly proposed and the error bounds are established. To correct the biases caused by the lasso penalty, a unified debiasing framework based on the decorrelated score equations is considered to establish asymptotic normality of the debiased lasso transfer AHR estimator. Confidence intervals and hypothesis tests for each component can be constructed. When the transferable sources are unknown, a data‐driven source detection algorithm is proposed with theoretical guarantee. Numerical studies verify the performance of our proposed estimator and confidence intervals, and an application to Genotype‐Tissue Expression data is also presented. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the sufficient dimension reduction problem in regression analysis with real‐valued response and functional or longitudinal covariates. We propose a new method based on gradients of the conditional distribution function to estimate the sufficient dimension reduction subspace. While existing inverse‐regression‐type methods relies on a linearity condition, our method is based on the gradient of conditional distribution function and its validity only requires smoothness conditions on the population parameters. Practically, the proposed estimator can be obtained by standard algorithm of functional principal component analysis. The proposed method is demonstrated through extensive simulations and two empirical examples. [ABSTRACT FROM AUTHOR]

There is a lack of point process models on linear networks. For an arbitrary linear network, we consider new models for a Cox process with an isotropic pair correlation function obtained in various ways by transforming an isotropic Gaussian process which is used for driving the random intensity function of the Cox process. In particular, we introduce three model classes given by log Gaussian, interrupted, and permanental Cox processes on linear networks, and consider for the first time statistical procedures and applications for parametric families of such models. Moreover, we construct new simulation algorithms for Gaussian processes on linear networks and discuss whether the geodesic metric or the resistance metric should be used for the kind of Cox processes studied in this paper. [ABSTRACT FROM AUTHOR]

In the past decade, various exact balancing‐based weighting methods were introduced to the causal inference literature. It eliminates covariate imbalance by imposing balancing constraints in a certain optimization problem, which can nevertheless be infeasible when there is bad overlap between the covariate distributions in the treated and control groups or when the covariates are high dimensional. Recently, approximate balancing was proposed as an alternative balancing framework. It resolves the feasibility issue by using inequality moment constraints instead. However, it can be difficult to select the threshold parameters. Moreover, moment constraints may not fully capture the discrepancy of covariate distributions. In this paper, we propose Mahalanobis balancing to approximately balance covariate distributions from a multivariate perspective. We use a quadratic constraint to control overall imbalance with a single threshold parameter, which can be tuned by a simple selection procedure. We show that the dual problem of Mahalanobis balancing is an ℓ2$$ {\ell}_2 $$ norm‐based regularized regression problem, and establish interesting connection to propensity score models. We derive asymptotic properties, discuss the high‐dimensional scenario, and make extensive numerical comparisons with existing balancing methods. [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]

Practical problems with missing data are common, and many methods have been developed concerning the validity and/or efficiency of statistical procedures. On a central focus, there have been longstanding interests on the mechanism governing data missingness, and correctly deciding the appropriate mechanism is crucially relevant for conducting proper practical investigations. In this paper, we present a new hypothesis testing approach for deciding between the conventional notions of missing at random and missing not at random in generalized linear models in the presence of instrumental variables. The foundational idea is to develop appropriate discrepancy measures between estimators whose properties significantly differ only when missing at random does not hold. We show that our testing approach achieves an objective data‐oriented choice between missing at random or not. We demonstrate the feasibility, validity, and efficacy of the new test by theoretical analysis, simulation studies, and a real data analysis. [ABSTRACT FROM AUTHOR]

The Lp$$ {L}^p $$‐quantile regression generalizes both quantile regression and expectile regression, and has become popular for its robustness and effectiveness especially when 1

Well‐recommended methods of forming "confidence intervals" for a binomial proportion give interval estimates that do not actually meet the definition of a confidence interval, in that their coverages are sometimes lower than the nominal confidence level. The methods are favoured because their intervals have a shorter average length than the Clopper–Pearson (gold‐standard) method, whose intervals really are confidence intervals. As the definition of a confidence interval is not being adhered to, another criterion for forming interval estimates for a binomial proportion is needed. In this paper, we suggest a new criterion for forming one‐sided intervals and equal‐tail two‐sided intervals. Methods which meet the criterion are said to yield locally correct confidence intervals. We propose a method that yields such intervals and prove that its intervals have a shorter average length than those of any other method that meets the criterion. Compared with the Clopper–Pearson method, the proposed method gives intervals with an appreciably smaller average length. For confidence levels of practical interest, the mid‐p method also satisfies the new criterion and has its own optimality property. It gives locally correct confidence intervals that are only slightly wider than those of the new method. [ABSTRACT FROM AUTHOR]

The estimation of absorption time distributions of Markov jump processes is an important task in various branches of statistics and applied probability. While the time‐homogeneous case is classic, the time‐inhomogeneous case has recently received increased attention due to its added flexibility and advances in computational power. However, commuting sub‐intensity matrices are assumed, which in various cases limits the parsimonious properties of the resulting representation. This paper develops the theory required to solve the general case through maximum likelihood estimation, and in particular, using the expectation‐maximization algorithm. A reduction to a piecewise constant intensity matrix function is proposed in order to provide succinct representations, where a parametric linear model binds the intensities together. Practical aspects are discussed and illustrated through the estimation of notoriously demanding theoretical distributions and real data, from the perspective of matrix analytic methods. [ABSTRACT FROM AUTHOR]

Isotonic regression or monotone function estimation is a problem of estimating function values under monotonicity constraints, which appears naturally in many scientific fields. This paper proposes a new Bayesian method with global–local shrinkage priors for estimating monotone function values. Specifically, we introduce half shrinkage priors for positive valued random variables and assign them for the first‐order differences of function values. We also develop fast and simple Gibbs sampling algorithms for full posterior analysis. By incorporating advanced shrinkage priors, the proposed method is adaptive to local abrupt changes or jumps in target functions. We show this adaptive property theoretically by proving that the posterior mean estimators are robust to large differences and that asymptotic risk for unchanged points can be improved. Finally, we demonstrate the proposed methods through simulations and applications to a real data set. [ABSTRACT FROM AUTHOR]

For the nonparametric regression models with covariates contaminated with the normal measurement errors, this paper proposes an extrapolation algorithm to estimate the regression functions. By applying the conditional expectation directly to the kernel‐weighted least squares of the deviations between the local linear approximation and the observed responses, the proposed algorithm successfully bypasses the simulation step in the classical simulation extrapolation, thus significantly reducing the computational time. It is noted that the proposed method also provides an exact form of the extrapolation function, although the extrapolation estimate generally cannot be obtained by simply setting the extrapolation variable to negative one in the fitted extrapolation function, if the bandwidth is less than the SD of the measurement error. Large sample properties of the proposed estimation procedure are discussed, as well as simulation studies and a real data example being conducted to illustrate its applications. [ABSTRACT FROM AUTHOR]

This paper considers distributed inference for two‐sample U‐statistics under the massive data setting. In order to reduce the computational complexity, this paper proposes distributed two‐sample U‐statistics and blockwise linear two‐sample U‐statistics. The blockwise linear two‐sample U‐statistic, which requires less communication cost, is more computationally efficient especially when the data are stored in different locations. The asymptotic properties of both types of distributed two‐sample U‐statistics are established. In addition, this paper proposes bootstrap algorithms to approximate the distributions of distributed two‐sample U‐statistics and blockwise linear two‐sample U‐statistics for both nondegenerate and degenerate cases. The distributed weighted bootstrap for the distributed two‐sample U‐statistic is new in the literature. The proposed bootstrap procedures are computationally efficient and are suitable for distributed computing platforms with theoretical guarantees. Extensive numerical studies illustrate that the proposed distributed approaches are feasible and effective. [ABSTRACT FROM AUTHOR]

This paper deals with a nonparametric Nadaraya–Watson (NW) estimator of the drift function computed from independent continuous observations of a diffusion process. Risk bounds on the estimator and its discrete‐time approximation are established. The paper also deals with extensions of the PCO and leave‐one‐out cross‐validation bandwidth selection methods for our NW estimator. Finally, some numerical experiments are provided. [ABSTRACT FROM AUTHOR]

We consider the construction of confidence bands for survival curves under the outcome‐dependent stratified sampling. A main challenge of this design is that data are a biased dependent sample due to stratification and sampling without replacement. Most literature on regression approximates this design by Bernoulli sampling but variance is generally overestimated. Even with this approximation, the limiting distribution of the inverse probability weighted Kaplan–Meier estimator involves a general Gaussian process, and hence quantiles of its supremum is not analytically available. In this paper, we provide a rigorous asymptotic theory for the weighted Kaplan–Meier estimator accounting for dependence in the sample. We propose the novel hybrid method to both simulate and bootstrap parts of the limiting process to compute confidence bands with asymptotically correct coverage probability. Simulation study indicates that the proposed bands are appropriate for practical use. A Wilms tumor example is presented. [ABSTRACT FROM AUTHOR]

In some clinical studies patient survival beyond a specific point in time, t0$$ {t}_0 $$, say, may be of special interest as it may for instance indicate patient cure. To analyze the t0$$ {t}_0 $$‐year risk for such patients may be accomplished using logistic regression with appropriate weights (IPWCC) that may further be augmented (AIPWCC) to improve efficiency. In this paper, we derive the most efficient estimator for this problem, which is different from the AIPWCC based on the full data efficient influence function. We first give the result for a survival endpoint and then generalize to the competing risk setting. The proposed estimators superior behavior is illustrated using simulations as well as applying it to some real data concerning the survival of blood and marrow transplanted patients. [ABSTRACT FROM AUTHOR]

In this paper, with an assumed parametric model for the selection probability function, a robust model averaging estimation method is proposed for partially linear models with responses missing at random. The method is based on a weighted Mallows‐type criterion. The method is robust in the sense that the asymptotic optimality holds true as long as the true model of the selection probability function is some measurable function of its assumed model. The optimal weight vector for model averaging is obtained by minimizing the weighted Mallows‐type criterion. It is shown that the robust model averaging method achieves the lowest possible squared error asymptotically. Some simulation studies were conducted to evaluate the proposed method. An application to two real examples are provided as illustration. [ABSTRACT FROM AUTHOR]

We consider Bayesian analysis on high‐dimensional spheres with angular central Gaussian priors. These priors model antipodally symmetric directional data, are easily defined in Hilbert spaces and occur, for instance, in Bayesian density estimation and binary level set inversion. In this paper we derive efficient Markov chain Monte Carlo methods for approximate sampling of posteriors with respect to these priors. Our approaches rely on lifting the sampling problem to the ambient Hilbert space and exploit existing dimension‐independent samplers in linear spaces. By a push‐forward Markov kernel construction we then obtain Markov chains on the sphere which inherit reversibility and spectral gap properties from samplers in linear spaces. Moreover, our proposed algorithms show dimension‐independent efficiency in numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, I consider a doubly stochastic Poisson process with intensity λt=qXt$$ {\lambda}_t=q\left({X}_t\right) $$ where X$$ X $$ is a continuous Itô semi‐martingale. Both processes are observed continuously over a fixed period 0,1$$ \left[0,1\right] $$. I propose a local polynomial estimator for the function q$$ q $$ on a given interval. Next, I propose a method to select the bandwidth in a nonasymptotic framework that leads to an oracle inequality. Considering the asymptotic n$$ n $$, and q=nq˜$$ q=n\tilde{q} $$, the accuracy of the proposed estimator over the Hölder class of order β$$ \beta $$ is n−β2β+1$$ {n}^{\frac{-\beta }{2\beta +1}} $$ if the degree of the chosen polynomial is greater than ⌊β⌋$$ \left\lfloor \beta \right\rfloor $$ and it is optimal in the minimax setting. I apply those results to data on French temperature and electricity spot prices from which I infer the intensity of electricity spot spikes as a function of the temperature. [ABSTRACT FROM AUTHOR]

This is a review paper, beginning with de Finetti's work on partial exchangeability, continuing with his approach to approximate exchangeability, and then his (surprising) approach to assigning informative priors in nonstandard situations. Recent progress on Markov chain Monte Carlo methods for drawing conclusions is supplemented by a review of work by Gerencsér and Ottolini on getting honest bounds for rates of convergence. The paper concludes with a speculative approach to combining classical asymptotics with Monte Carlo. This promises real speed‐ups and makes a nice example of how theory and computation can interact. [ABSTRACT FROM AUTHOR]

This paper introduces a new modeling and inference framework for multivariate and anisotropic point processes. Building on recent innovations in multivariate spatial statistics, we propose a new family of multivariate anisotropic random fields, and from them a family of anisotropic point processes. We give conditions that make the proposed models valid. We also propose a Palm likelihood‐based inference method for this type of point process, circumventing issues of likelihood tractability. Finally we illustrate the utility of the proposed modeling framework by analyzing spatial ecological observations of plants and trees in the Barro Colorado Island data. [ABSTRACT FROM AUTHOR]

Spatial econometric models estimated on the big geo‐located point data have at least two problems: limited computational capabilities and inefficient forecasting for the new out‐of‐sample geo‐points. This is because of spatial weights matrix W defined for in‐sample observations only and the computational complexity. Machine learning models suffer the same when using kriging for predictions; thus this problem still remains unsolved. The paper presents a novel methodology for estimating spatial models on big data and predicting in new locations. The approach uses bootstrap and tessellation to calibrate both model and space. The best bootstrapped model is selected with the PAM (Partitioning Around Medoids) algorithm by classifying the regression coefficients jointly in a nonindependent manner. Voronoi polygons for the geo‐points used in the best model allow for a representative space division. New out‐of‐sample points are assigned to tessellation tiles and linked to the spatial weights matrix as a replacement for an original point what makes feasible usage of calibrated spatial models as a forecasting tool for new locations. There is no trade‐off between forecast quality and computational efficiency in this approach. An empirical example illustrates a model for business locations and firms' profitability. [ABSTRACT FROM AUTHOR]

The envelope method produces efficient estimation in multivariate linear regression, and is widely applied in biology, psychology, and economics. This paper estimates parameters through a model averaging methodology and promotes the predicting abilities of the envelope models. We propose a frequentist model averaging method by minimizing a cross‐validation criterion. When all the candidate models are misspecified, the proposed model averaging estimator is proved to be asymptotically optimal. When correct candidate models exist, the coefficient estimator is proved to be consistent, and the sum of the weights assigned to the correct models, in probability, converges to one. Simulations and an empirical application demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Gibbs point processes (GPPs) constitute a large and flexible class of spatial point processes with explicit dependence between the points. They can model attractive as well as repulsive point patterns. Feature selection procedures are an important topic in high‐dimensional statistical modeling. In this paper, a composite likelihood (in particular pseudo‐likelihood) approach regularized with convex and nonconvex penalty functions is proposed to handle statistical inference for possibly high‐dimensional inhomogeneous GPPs. We particularly investigate the setting where the number of covariates diverges as the domain of observation increases. Under some conditions provided on the spatial GPP and on penalty functions, we show that the oracle property, consistency and asymptotic normality hold. Our results also cover the low‐dimensional case which fills a large gap in the literature. Through simulation experiments, we validate our theoretical results and finally, an application to a tropical forestry dataset illustrates the use of the proposed approach. [ABSTRACT FROM AUTHOR]

In the paper we derive new types of multivariate exponentially weighted moving average (EWMA) control charts which are based on the Euclidean distance and on the distance defined by using the inverse of the diagonal matrix consisting of the variances. The design of the proposed control schemes does not involve the computation of the inverse covariance matrix and, thus, it can be used in the high‐dimensional setting. The distributional properties of the control statistics are obtained and are used in the determination of the new control procedures. Within an extensive simulation study, the new approaches are compared with the multivariate EWMA control charts which are based on the Mahalanobis distance. [ABSTRACT FROM AUTHOR]

This paper provides a set of uniform consistency results with rates for nonparametric density and regression estimators smoothed by the beta kernel having support on the unit interval. Weak and strong uniform convergence is explored on the basis of expanding compact sets and general sequences of smoothing parameters. The results in this paper are useful for asymptotic analysis of two‐step semiparametric estimation using a first‐step kernel estimate as a plug‐in. We provide simulations and a real data example illustrating attractive properties of the estimators. [ABSTRACT FROM AUTHOR]

Continuous‐time autoregressive processes have been applied successfully in many fields and are particularly advantageous in the modeling of irregularly spaced or high‐frequency time series data. A convenient nonlinear extension of this model are continuous‐time threshold autoregressions (CTAR). CTAR allow for greater flexibility in model parameters and can represent a regime switching behavior. However, so far only Gaussian CTAR processes have been defined, so that this model class could not be used for data with jumps, as frequently observed in financial applications. Hence, as a novelty, we construct CTAR processes with jumps in this paper. Existence of a unique weak solution and weak consistency of an Euler approximation scheme is proven. As a closed form expression of the likelihood is not available, we use kernel‐based particle filtering for estimation. We fit our model to the Physical Electricity Index and show that it describes the data better than other comparable approaches. [ABSTRACT FROM AUTHOR]

We consider model selection for linear mixed‐effects models with clustered structure, where conditional Kullback–Leibler (CKL) loss is applied to measure the efficiency of the selection. We estimate the CKL loss by substituting the empirical best linear unbiased predictors (EBLUPs) into random effects with model parameters estimated by maximum likelihood. Although the BLUP approach is commonly used in predicting random effects and future observations, selecting random effects to achieve asymptotic loss efficiency concerning CKL loss is challenging and has not been well studied. In this paper, we propose addressing this difficulty using a conditional generalized information criterion (CGIC) with two tuning parameters. We further consider a challenging but practically relevant situation where the number, m$$ m $$, of clusters does not go to infinity with the sample size. Hence the random‐effects variances are not consistently estimable. We show that via a novel decomposition of the CKL risk, the CGIC achieves consistency and asymptotic loss efficiency, whether m$$ m $$ is fixed or increases to infinity with the sample size. We also conduct numerical experiments to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

Simultaneous inference allows for the exploration of data while deciding on criteria for proclaiming discoveries. It was recently proved that all admissible post hoc inference methods for the true discoveries must employ closed testing. In this paper, we investigate efficient closed testing with local tests of a special form: thresholding a function of sums of test scores for the individual hypotheses. Under this special design, we propose a new statistic that quantifies the cost of multiplicity adjustments, and we develop fast (mostly linear‐time) algorithms for post hoc inference. Paired with recent advances in global null tests based on generalized means, our work instantiates a series of simultaneous inference methods that can handle many dependence structures and signal compositions. We provide guidance on the method choices via theoretical investigation of the conservativeness and sensitivity for different local tests, as well as simulations that find analogous behavior for local tests and full closed testing. [ABSTRACT FROM AUTHOR]

In this paper, we propose new asymptotic confidence intervals for extreme quantiles, that is, for quantiles located outside the range of the available data. We restrict ourselves to the situation where the underlying distribution is heavy‐tailed. While asymptotic confidence intervals are mostly constructed around a pivotal quantity, we consider here an alternative approach based on the distribution of order statistics sampled from a uniform distribution. The convergence of the coverage probability to the nominal one is established under a classical second‐order condition. The finite sample behavior is also examined and our methodology is applied to a real dataset. [ABSTRACT FROM AUTHOR]

The empirical best linear unbiased predictor (EBLUP) is a linear shrinkage of the direct estimate toward the regression estimate and useful for the small area estimation in the sense of increasing precision of estimation of small area means. However, one potential difficulty of EBLUP is that the overall estimate for a larger geographical area based on a sum of EBLUP is not necessarily identical to the corresponding direct estimate like the overall sample mean. To fix this problem, the paper suggests a new method for benchmarking EBLUP in the Fay–Herriot model without assuming normality of random effects and sampling errors. The resulting benchmarked empirical linear shrinkage (BELS) predictor has novelty in the sense that coefficients for benchmarking are adjusted based on the data from each area. To measure the uncertainty of BELS, the second‐order unbiased estimator of the mean squared error is derived. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of simultaneous variable selection and estimation in the random‐intercepts model with the first‐order lag response. This type of model is commonly used for analyzing longitudinal data obtained through repeated measurements on individuals over time. This model uses random effects to cover the intra‐class correlation, and the first lagged response to address the serial correlation, which are two common sources of dependency in longitudinal data. We demonstrate that the conditional likelihood approach by ignoring correlation among random effects and initial responses can lead to biased regularized estimates. Furthermore, we demonstrate that joint modeling of initial responses and subsequent observations in the structure of dynamic random‐intercepts models leads to both consistency and Oracle properties of regularized estimators. We present theoretical results in both low‐ and high‐dimensional settings and evaluate regularized estimators' performances by conducting simulation studies and analyzing a real dataset. Supporting information is available online. [ABSTRACT FROM AUTHOR]

Many neuroscience experiments record sequential trajectories where each trajectory consists of oscillations and fluctuations around zero. Such trajectories can be viewed as zero‐mean functional data. When there are structural breaks in higher‐order moments, it is not always easy to spot these by mere visual inspection. Motivated by this challenging problem in brain signal analysis, we propose a detection and testing procedure to find the change point in functional covariance. The detection procedure is based on the cumulative sum statistics (CUSUM). The fully functional testing procedure relies on a null distribution which depends on infinitely many unknown parameters, though in practice only a finite number of these parameters can be included for the hypothesis test of the existence of change point. This paper provides some theoretical insights on the influence of the number of parameters. Meanwhile, the asymptotic properties of the estimated change point are developed. The effectiveness of the proposed method is numerically validated in simulation studies and an application to investigate changes in rat brain signals following an experimentally‐induced stroke. [ABSTRACT FROM AUTHOR]

This paper deals with the specification of probability distributions expressing ignorance concerning annual or otherwise discretized failure or mortality rates, when these rates can safely be assumed to be increasing and convex, but are completely unknown otherwise. Such distributions can be used as noninformative priors for Bayesian analysis of failure data. We demonstrate why a uniform distribution used in earlier work is unsatisfactory, especially from the point of view of insensitivity with respect to the time scale that is chosen for the problem at hand. We suggest alternative distributions based on Dirichlet distributed weights for the extreme points of relevant convex sets, and discuss which consequences a requirement for scale neutrality has for the choice of Dirichlet parameters. [ABSTRACT FROM AUTHOR]

Remove unwanted variation (RUV) is an estimation and normalization system in which the underlying correlation structure of a multivariate dataset is estimated from negative control measurements, typically gene expression values, which are assumed to stay constant across experimental conditions. In this paper we derive the weight matrix which is estimated and incorporated into the generalized least squares estimates of RUV‐inverse, and show that this weight matrix estimates the average covariance matrix across negative control measurements. RUV‐inverse can thus be viewed as an estimation method adjusting for an unknown experimental design. We show that for a balanced incomplete block design (BIBD), RUV‐inverse recovers intra‐ and interblock estimates of the relevant parameters and combines them as a weighted sum just like the best linear unbiased estimator (BLUE), except that the weights are globally estimated from the negative control measurements instead of being individually optimized to each measurement as in the classical, single measurement BIBD BLUE. [ABSTRACT FROM AUTHOR]

This paper introduces empirical best predictors of small area bivariate parameters, like ratios of sums or sums of ratios, by assuming that the target unit‐level vector follows a bivariate nested error regression model. The corresponding means squared errors are estimated by parametric bootstrap. Several simulation experiments empirically study the behavior of the introduced statistical methodology. An application to real data from the Spanish household budget survey gives estimators of ratios of food household expenditures by provinces. [ABSTRACT FROM AUTHOR]

Randomly censored survival data appear in a wide variety of applications in which the time until the occurrence of a certain event is not completely observable. In this paper, we assume that the statistician observes a possibly censored survival time along with a censoring indicator. In this setting, we study a class of M‐estimators with a bounded influence function, in the spirit of the infinitesimal approach to robustness. We outline the main asymptotic properties of the robust M‐estimators and characterize the optimal B‐robust estimator according to two possible measures of sensitivity. Building on these results, we define robust testing procedures which are natural counterparts to the classical Wald, score, and likelihood ratio tests. The empirical performance of our robust estimators and tests is assessed in two extensive simulation studies. An application to data from a well‐known medical study on head and neck cancer is also presented. [ABSTRACT FROM AUTHOR]

In short‐term nonlife (e.g., car and homeowner) insurance, policies are renewed yearly. Insurance companies typically keep track of each policyholder's claims per year, resulting in longitudinal data. Efficient modeling of time dependence in longitudinal claim data will improve the prediction of future claims needed for routine actuarial practice, such as ratemaking. Insurance claim data usually follow a two‐part mixed distribution: a probability mass at zero corresponding to no claim and an otherwise positive claim from a skewed and long‐tailed distribution. This two‐part data structure leads to difficulties in applying established models for longitudinal data. In this paper, we propose a two‐part D‐vine copula model to study longitudinal mixed claim data. We build two stationary D‐vine copulas. One is used to model the time dependence in binary outcomes resulting from whether or not a claim has occurred. The other studies the dependence in the claim size given occurrence. Under the proposed model, the prediction of the probability of making claims and the quantiles of severity given occurrence is straightforward. We use our approach to investigate a dataset from the Local Government Property Insurance Fund in the state of Wisconsin. [ABSTRACT FROM AUTHOR]

This paper introduces tests for the symmetry of the copula of random vector. The proposed statistics are based on the copula characteristic function and the weight function that appears naturally in their definition are assumed to belong to the general family of Lévy measures. The proposed test statistics are rank‐based and expresses as weighted L2‐norms computed from a vector of empirical copula characteristic functions. Their nondegenerate asymptotic distributions under the null hypothesis and general alternatives, as well as the validity of a multiplier bootstrap for the computation of p‐values, are derived using nonstandard arguments. Extended Monte–Carlo experiments show that the new tests hold their size well and are powerful against a wide range of alternatives, and appear to be more powerful than a Cramér–von Mises test based on empirical copulas. [ABSTRACT FROM AUTHOR]