Sampling without replacement from a high-dimensional finite population

IF 1.5 2区数学 Q2 STATISTICS & PROBABILITY

Bernoulli Pub Date : 2023-01-27 DOI:10.3150/22-bej1580

Jiang Hu, Shao-An Wang, Yangchun Zhang, Wang Zhou

引用次数: 1

Abstract

It is well known that most of the existing theoretical results in statistics are based on the assumption that the sample is generated with replacement from an infinite population. However, in practice, available samples are almost always collected without replacement. If the population is a finite set of real numbers, whether we can still safely use the results from samples drawn without replacement becomes an important problem. In this paper, we focus on the eigenvalues of high-dimensional sample covariance matrices generated without replacement from finite populations. Specifically, we derive the Tracy-Widom laws for their largest eigenvalues and apply these results to parallel analysis. We provide new insight into the permutation methods proposed by Buja and Eyuboglu in [Multivar Behav Res. 27(4) (1992) 509--540]. Simulation and real data studies are conducted to demonstrate our results.

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从高维有限总体中进行无替换采样

众所周知，统计学中现有的大多数理论结果都是基于这样的假设，即样本是由无限总体替换产生的。然而，在实践中，可用的样品几乎总是收集而不替换。如果总体是有限实数的集合，我们是否仍然可以安全地使用抽取的样本的结果而不进行替换就成为一个重要的问题。本文主要研究由有限总体生成的不替换的高维样本协方差矩阵的特征值问题。具体来说，我们导出了它们的最大特征值的tracy - wisdom定律，并将这些结果应用于并行分析。我们对Buja和Eyuboglu在[Multivar Behav Res. 27(4)(1992) 509—540]中提出的置换方法提供了新的见解。通过仿真和实际数据研究验证了本文的研究结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Bernoulli 数学-统计学与概率论

CiteScore

3.40

自引率

0.00%

发文量

116

审稿时长

6-12 weeks

期刊介绍： BERNOULLI is the journal of the Bernoulli Society for Mathematical Statistics and Probability, issued four times per year. The journal provides a comprehensive account of important developments in the fields of statistics and probability, offering an international forum for both theoretical and applied work. BERNOULLI will publish: Papers containing original and significant research contributions: with background, mathematical derivation and discussion of the results in suitable detail and, where appropriate, with discussion of interesting applications in relation to the methodology proposed. Papers of the following two types will also be considered for publication, provided they are judged to enhance the dissemination of research: Review papers which provide an integrated critical survey of some area of probability and statistics and discuss important recent developments. Scholarly written papers on some historical significant aspect of statistics and probability.