Tests for high-dimensional generalized linear models under general covariance structure

IF 1.5 3区数学 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computational Statistics & Data Analysis Pub Date : 2024-07-17 DOI:10.1016/j.csda.2024.108026

Weichao Yang , Xu Guo , Lixing Zhu

引用次数: 0

Abstract

This study investigates the testing of regression coefficients within high-dimensional generalized linear models featuring general covariance structures. The derived asymptotic properties reveal that distinct covariance structures can lead to varying limiting null distributions, including the normal distribution, for a widely employed quadratic-norm based test statistic. This circumstance renders it infeasible to determine critical values through a limiting null distribution. In response to this challenge, we propose a multiplier bootstrap test procedure for practical implementation. Additionally, we introduce a modified version of this procedure, incorporating projection when dealing with nuisance parameters. We then proceed to examine the asymptotic level and power of the proposed tests and assess their finite-sample performance through simulations. Finally, we present a real data analysis to illustrate the practical application of the proposed tests.

查看原文本刊更多论文

一般协方差结构下的高维广义线性模型试验

本研究探讨了具有一般协方差结构的高维广义线性模型中回归系数的检验问题。推导出的渐近性质表明，对于广泛使用的基于二次正态分布的检验统计量，不同的协方差结构会导致不同的极限零分布，包括正态分布。这种情况使得通过极限空分布确定临界值变得不可行。为了应对这一挑战，我们提出了一种乘数自举检验程序，以便实际应用。此外，我们还介绍了该程序的修改版，在处理骚扰参数时加入了投影。然后，我们继续检验所提出检验的渐近水平和功率，并通过模拟评估其有限样本性能。最后，我们通过实际数据分析来说明所提检验的实际应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Computational Statistics & Data Analysis 数学-计算机：跨学科应用

CiteScore

3.70

自引率

5.60%

发文量

167

审稿时长

60 days

期刊介绍： Computational Statistics and Data Analysis (CSDA), an Official Publication of the network Computational and Methodological Statistics (CMStatistics) and of the International Association for Statistical Computing (IASC), is an international journal dedicated to the dissemination of methodological research and applications in the areas of computational statistics and data analysis. The journal consists of four refereed sections which are divided into the following subject areas: I) Computational Statistics - Manuscripts dealing with: 1) the explicit impact of computers on statistical methodology (e.g., Bayesian computing, bioinformatics,computer graphics, computer intensive inferential methods, data exploration, data mining, expert systems, heuristics, knowledge based systems, machine learning, neural networks, numerical and optimization methods, parallel computing, statistical databases, statistical systems), and 2) the development, evaluation and validation of statistical software and algorithms. Software and algorithms can be submitted with manuscripts and will be stored together with the online article. II) Statistical Methodology for Data Analysis - Manuscripts dealing with novel and original data analytical strategies and methodologies applied in biostatistics (design and analytic methods for clinical trials, epidemiological studies, statistical genetics, or genetic/environmental interactions), chemometrics, classification, data exploration, density estimation, design of experiments, environmetrics, education, image analysis, marketing, model free data exploration, pattern recognition, psychometrics, statistical physics, image processing, robust procedures. [...] III) Special Applications - [...] IV) Annals of Statistical Data Science [...]