Weighted bootstrap for two-sample U-statistics

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Statistical Planning and Inference Pub Date : 2023-09-01 DOI:10.1016/j.jspi.2023.02.004

Bingyao Huang , Yanyan Liu , Liuhua Peng

引用次数: 0

Abstract

In this paper, we introduce weighted bootstrap algorithms for both non-degenerate and degenerate two-sample $U$ -statistics with arbitrary degrees. For the non-degenerate case, weighted bootstrap with dependent weights is introduced as a generalization of Efron’s conventional bootstrap. In addition, two weighted bootstrap procedures with independent productive weights and independent additive weights are proposed under non-degeneracy. More importantly, we extend the weighted bootstrap method to two-sample $U$ -statistics under the degeneracy of order 2 with a novel construction of random weights. Theoretical supports of the proposed weighted bootstrap procedures under non-degeneracy and degeneracy of order 2 are established. Numerical studies illustrate that the proposed approaches are feasible and effective for statistical inferences.

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两样本u统计量的加权自举

本文介绍了任意度非退化和退化两样本u统计量的加权自举算法。对于非退化情况，引入了权相关的加权自举法，作为Efron传统自举法的推广。此外，在非退化条件下，提出了两个具有独立生产权和独立加性权的加权自举过程。更重要的是，我们用一种新的随机权的构造将加权自举法推广到退化为2阶的两样本u统计量。在非简并度和简并度为2阶的情况下，给出了加权自举过程的理论支持。数值研究表明，该方法对统计推断是可行和有效的。

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

Journal of Statistical Planning and Inference 数学-统计学与概率论

CiteScore

2.10

自引率

11.10%

发文量

审稿时长

3-6 weeks

期刊介绍： The Journal of Statistical Planning and Inference offers itself as a multifaceted and all-inclusive bridge between classical aspects of statistics and probability, and the emerging interdisciplinary aspects that have a potential of revolutionizing the subject. While we maintain our traditional strength in statistical inference, design, classical probability, and large sample methods, we also have a far more inclusive and broadened scope to keep up with the new problems that confront us as statisticians, mathematicians, and scientists. We publish high quality articles in all branches of statistics, probability, discrete mathematics, machine learning, and bioinformatics. We also especially welcome well written and up to date review articles on fundamental themes of statistics, probability, machine learning, and general biostatistics. Thoughtful letters to the editors, interesting problems in need of a solution, and short notes carrying an element of elegance or beauty are equally welcome.