TY - JOUR

T1 - Pairwise distance-based tests for conditional symmetry

AU - Niu, Cuizhen

AU - Guo, Xu

AU - Li, Yong

AU - ZHU, Lixing

N1 - Funding Information:
The authors are grateful to the editor, the associate editor and the anonymous referee for the constructive comments and suggestions that led to significant improvement of an early manuscript. The research described herewith was supported by National Natural Science Foundation of China NSFC ( 11701034 , 11601227 , 11626130 , 11671042 ), the Fundamental Research Funds for the Central Universities, China Postdoctoral Science Foundation ( 2016M600951 , 2017M610058 ) and a grant from the University Grants Council of Hong Kong.

PY - 2018/12

Y1 - 2018/12

N2 - In this paper, we develop a pairwise distance-based testing procedure for conditional symmetry of a random vector given another random vector and apply it to the cases with given and unknown center that is a parametric regression function, respectively. The resulting tests are moments-based and thus the curse of dimensionality can then be greatly alleviated. The asymptotic properties of the test statistics are investigated. The tests can detect local alternatives distinct from the null at a fastest possible convergence rate in hypothesis testing. To determine critical values, a Monte Carlo-based approximation to the limiting null distributions is suggested. We prove that the approximation works even under local alternative hypotheses. Some simulation studies and a real data example are conducted to examine the performance of the tests.

AB - In this paper, we develop a pairwise distance-based testing procedure for conditional symmetry of a random vector given another random vector and apply it to the cases with given and unknown center that is a parametric regression function, respectively. The resulting tests are moments-based and thus the curse of dimensionality can then be greatly alleviated. The asymptotic properties of the test statistics are investigated. The tests can detect local alternatives distinct from the null at a fastest possible convergence rate in hypothesis testing. To determine critical values, a Monte Carlo-based approximation to the limiting null distributions is suggested. We prove that the approximation works even under local alternative hypotheses. Some simulation studies and a real data example are conducted to examine the performance of the tests.

KW - Conditional symmetry

KW - Nonparametric testing

KW - Pairwise distance

UR - http://www.scopus.com/inward/record.url?scp=85050307630&partnerID=8YFLogxK

U2 - 10.1016/j.csda.2018.06.018

DO - 10.1016/j.csda.2018.06.018

M3 - Article

AN - SCOPUS:85050307630

VL - 128

SP - 145

EP - 162

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

SN - 0167-9473

ER -