距离相关存在测量误差

IF 1.6 3区数学 Q2 STATISTICS & PROBABILITY

Journal of Multivariate Analysis Pub Date : 2026-01-01 Epub Date: 2025-11-03 DOI:10.1016/j.jmva.2025.105518

Xilin Zhang , Guoliang Fan , Liping Zhu

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引用次数: 0

摘要

独立性检验是统计学中的一个基本问题。实际上，几乎所有的观测结果都带有随机误差。存在测量误差的独立性检验是一个重要的问题，但在文献中很少涉及。本文主要研究存在测量误差时的距离相关问题。我们表明，距离协方差在存在测量误差时被低估，并且是测量误差分散的严格递减函数。此外，基于距离协方差和距离相关的独立性检验的幂都是测量误差离散度的严格递减函数。大量的数值模拟和实际数据分析支持了本文的结论。

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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Distance correlation in the presence of measurement errors

Independence testing is a fundamental issue in statistics. In practice, almost all observations are measured with random errors. The independence test in the presence of measurement errors is an important issue but is rarely addressed in the literature. This paper focuses on distance correlation in the presence of measurement errors. We show that distance covariance is underestimated in the presence of measurement errors and is a strictly decreasing function of the dispersion of measurement errors. Furthermore, the powers of independence tests based on distance covariance and distance correlation are both strictly decreasing functions of the dispersion of measurement errors. Extensive numerical simulations and real data analysis support the conclusions drawn in this paper.

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来源期刊

Journal of Multivariate Analysis 数学-统计学与概率论

CiteScore

2.40

自引率

25.00%

发文量

108

审稿时长

74 days

期刊介绍： Founded in 1971, the Journal of Multivariate Analysis (JMVA) is the central venue for the publication of new, relevant methodology and particularly innovative applications pertaining to the analysis and interpretation of multidimensional data. The journal welcomes contributions to all aspects of multivariate data analysis and modeling, including cluster analysis, discriminant analysis, factor analysis, and multidimensional continuous or discrete distribution theory. Topics of current interest include, but are not limited to, inferential aspects of Copula modeling Functional data analysis Graphical modeling High-dimensional data analysis Image analysis Multivariate extreme-value theory Sparse modeling Spatial statistics.