Journal of Statistical Planning and Inference最新文献

Maximum correntropy criterion regression (MCCR) models have been well studied within the theoretical framework of statistical learning when the scale parameters take fixed values or go to infinity. This paper studies MCCR models with tending-to-zero scale parameters. It is revealed that the optimal learning rate of MCCR models is $O\left(n^{-1}\right)$ in the asymptotic sense when the sample size $n$ goes to infinity. In the case of finite samples, the performance and robustness of MCCR, Huber and the least square regression models are compared. The applications of these three methods to real data are also demonstrated.

We investigate the validity of two resampling techniques when carrying out inference on the underlying unknown copula using a recently proposed class of smooth, possibly data-adaptive nonparametric estimators that contains empirical Bernstein copulas (and thus the empirical beta copula). Following Kiriliouk et al. (2021), the first resampling technique is based on drawing samples from the smooth estimator and can only can be used in the case of independent observations. The second technique is a smooth extension of the so-called sequential dependent multiplier bootstrap and can thus be used in a time series setting and, possibly, for change-point analysis. The two studied resampling schemes are applied to confidence interval construction and the offline detection of changes in the cross-sectional dependence of multivariate time series, respectively. Monte Carlo experiments confirm the possible advantages of such smooth inference procedures over their non-smooth counterparts. A by-product of this work is the study of the weak consistency and finite-sample performance of two classes of smooth estimators of the first-order partial derivatives of a copula which can have applications in mean and quantile regression.

Multivariate functional data are prevalent in various fields such as biology, climatology, and finance. Motivated by the World Health Data applications, in this study, we propose and examine a global test for assessing the equality of multiple mean functions in multivariate functional data. This test addresses the one-way Functional Multivariate Analysis of Variance (FMANOVA) problem, which is a fundamental issue in the analysis of multivariate functional data. While numerous analysis of variance tests have been proposed and studied for univariate functional data, only a limited number of methods have been developed for the one-way FMANOVA problem. Furthermore, our global test has the ability to handle heteroscedasticity in the unknown covariance function matrices that underlie the multivariate functional data, which is not possible with existing methods. We establish the asymptotic null distribution of the test statistic as a chi-squared-type mixture, which depends on the eigenvalues of the covariance function matrices. To approximate the null distribution, we introduce a Welch–Satterthwaite type chi-squared-approximation with consistent parameter estimation. The proposed test exhibits root-$n$ consistency, meaning it possesses nontrivial power against a local alternative. Additionally, it offers superior computational efficiency compared to several permutation-based tests. Through simulation studies and applications to the World Health Data, we highlight the advantages of our global test.

Misclassification of binary responses, if ignored, may severely bias the maximum likelihood estimators (MLEs) of regression parameters. For such data, a binary regression model incorporating non-differential classification errors is extensively used by researchers in different application contexts. We strongly caution against indiscriminate use of this model considering the fact that it suffers from a serious estimation problem due to confounding of the unknown misclassification probabilities with the regression parameters, and thus, may lead to a highly biased estimate. To overcome this problem, we propose here the use of an internal validation sample in addition to the main sample. Assuming differential classification errors, we consider MLEs of the regression parameters based on the joint likelihood of the main sample and the internal validation sample. We then develop a rigorous asymptotic theory for the joint MLEs under standard assumptions. To facilitate its easy implementation for inference, we propose a bootstrap approximation to the asymptotic distribution and prove its consistency. The results of the simulation studies suggest that even an extremely small validation sample may lead to a vastly improved inference. Finally, the methodology is illustrated with a real-life survey data.

Modern experiments typically involve a very large number of variables. Screening designs allow experimenters to identify active factors in a minimum number of trials. To save costs, only low-level factorial designs are considered for screening experiments, especially two- and three-level designs. In this article, we provide a systematic method to construct screening designs that contain both two- and three-level factors based on Hadamard matrices with the fold-over structure. The proposed designs have good performance in terms of D-optimal and A-optimal criteria, and the estimates of the main effects are unbiased by the second-order effects, making them very suitable for screening experiments. Besides, some theoretical results on D- and A-optimality are obtained as a by-product.

Missing data is a common problem in real data analysis. In this paper, a Mallows model averaging method based on kernel regression imputation is proposed for the linear regression models with responses missing at random. We prove that our method asymptotically achieves the lowest possible squared error. Compared with the existing model averaging methods, the new method does not require the use of a parameter model to characterize the missing generation mechanism. The Monte Carlo simulation and a practical application demonstrate the usefulness of the proposed method.

The categorical Gini correlation, ${\rho }_g$, was proposed by Dang et al. (2021) to measure the dependence between a categorical variable, $Y$, and a numerical variable, $X$. It has been shown that ${\rho }_g$ has more appealing properties than current existing dependence measurements. In this paper, we develop the jackknife empirical likelihood (JEL) method for ${\rho }_g$. Confidence intervals for the Gini correlation are constructed without estimating the asymptotic variance. Adjusted and weighted JEL are explored to improve the performance of the standard JEL. Simulation studies show that our methods are competitive to existing methods in terms of coverage accuracy and shortness of confidence intervals. The proposed methods are illustrated in an application on two real datasets.

The construction of objective priors is, at best, challenging for multidimensional parameter spaces. A common practice is to assume independence and set up the joint prior as the product of marginal distributions obtained via “standard” objective methods, such as Jeffreys or reference priors. However, the assumption of independence a priori is not always reasonable, and whether it can be viewed as strictly objective is still open to discussion. In this paper, by extending a previously proposed objective approach based on scoring rules for the one dimensional case, we propose a novel objective prior for multidimensional parameter spaces which yields a dependence structure. The proposed prior has the appealing property of being proper and does not depend on the chosen model; only on the parameter space considered.

Classical functional linear regression models the relationship between a scalar response and a functional covariate, where the coefficient function is assumed to be identical for all subjects. In this paper, the classical model is extended to allow heterogeneous coefficient functions across different subgroups of subjects. The greatest challenge is that the subgroup structure is usually unknown to us. To this end, we develop a penalization-based approach which innovatively applies the penalized fusion technique to simultaneously determine the number and structure of subgroups and coefficient functions within each subgroup. An effective computational algorithm is derived. We also establish the oracle properties and estimation consistency. Extensive numerical simulations demonstrate its superiority compared to several competing methods. The analysis of an air quality dataset leads to interesting findings and improved predictions.

The fixed-X knockoff filter is a flexible framework for variable selection with false discovery rate (FDR) control in linear models with arbitrary design matrices (of full column rank) and it allows for finite-sample selective inference via the Lasso estimates. In this paper, we extend the theory of the knockoff procedure to tests with composite null hypotheses, which are usually more relevant to real-world problems. The main technical challenge lies in handling composite nulls in tandem with dependent features from arbitrary designs. We develop two methods for composite inference with the knockoffs, namely, shifted ordinary least-squares (S-OLS) and feature-response product perturbation (FRPP), building on new structural properties of test statistics under composite nulls. We also propose two heuristic variants of S-OLS method that outperform the celebrated Benjamini–Hochberg (BH) procedure for composite nulls, which serves as a heuristic baseline under dependent test statistics. Finally, we analyze the loss in FDR when the original knockoff procedure is naively applied on composite tests.