Independence tests in the presence of measurement errors: An invariance law

JOURNAL OF MULTIVARIATE ANALYSIS

卷:188

Article

Fan, Jinlin¹  Zhang, Yaowu²  Zhu, Liping¹ 

[1] Renmin Univ China, Inst Stat & Big Data, Ctr Appl Stat, Beijing 100872, Peoples R China

[2] Shanghai Univ Finance & Econ, Sch Informat Management & Engn, Res Inst Interdisciplinary Sci, Shanghai 200433, Peoples R China

关键词: Distance correlation;    Independence test;    Measurement error;    Nonlinear dependence;   

DOI  :  10.1016/j.jmva.2021.104818

来源: Elsevier

【 摘 要 】

In many scientific areas the observations are collected with measurement errors. We are interested in measuring and testing independence between random vectors which are subject to measurement errors. We modify the weight functions in the classic distance covariance such that, the modified distance covariance between the random vectors of primary interest is the same as its classic version between the surrogate random vectors, which is referred to as the invariance law in the present context. The presence of measurement errors may substantially weaken the degree of nonlinear dependence. An immediate issue arises: The classic distance correlation between the surrogate vectors cannot reach one even if the two random vectors of primary interest are exactly linearly dependent. To address this issue, we propose to estimate the distance variance using repeated measurements. We study the asymptotic properties of the modified distance correlation thoroughly. In addition, we demonstrate its finite-sample performance through extensive simulations and a real-world application. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free