A Class of Robust Independence Tests Based on Weighted Integrals of Empirical Characteristic Functions  

作　　者：Feng ZOU Chang Liang ZOU Heng Jian CUI 

机构地区：[1]School of Statistics and Mathematics,Zhongnan University of Economics and Law,Wuhan,430073,P.R.China [2]NITFID,School of Statistics and Data Science,LPMC and KLMDASR and LEBPS,Nankai University,Tianjin,300071,P.R.China [3]School of Mathematical Sciences,Capital Normal University,Beijing,100048,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第12期2921-2952,共32页数学学报（英文版）

基　　金：supported by National Natural Science Foundation of China(NNSFC)(Grant No.12201317);China Postdoctoral Science Foundation(Grant No.2022M721716),Changliang Zou’s research was supported by the National Key R&D Program of China(Grant Nos.2022YFA1003703,2022YFA1003800);the National Natural Science Foundation of China(Grant Nos.11925106,12231011,11931001,12226007,12326325);Cui’s research was supported by NNSFC(Grant Nos.12031016 and 11971324)。

摘　　要：In this paper,we propose a class of robust independence tests for two random vectors based on weighted integrals of empirical characteristic functions.By letting weight functions be probability density functions of a class of special distributions,the proposed test statistics have simple closed forms and do not require moment conditions on the random vectors.Moreover,we derive the asymptotic distributions of the test statistics under the null hypothesis.The proposed testing method is computationally feasible and easy to implement.Based on a data-driven bandwidth selection method,Monte Carlo simulation studies indicate that our tests have a relatively good performance compared with the competitors.A real data example is also presented to illustrate the application of our tests.

关 键 词：Asymptotic properties DATA-DRIVEN robust independence tests special distributions weighted integrals 

分 类 号：O212.1[理学—概率论与数理统计]