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HIGH-ORDER CONDITIONAL DISTANCE COVARIANCE WITH CONDITIONAL MUTUAL INDEPENDENCE

Published online by Cambridge University Press:  27 July 2020

Pengfei Liu ,
Xuejun Ma Open the ORCID record for Xuejun Ma [Opens in a new window]  and
Wang Zhou
Pengfei Liu
Affiliation:
School of Mathematics and Statistics and Research Institute of Mathematical Sciences (RIMS), Jiangsu Normal University, 101 Shanghai Road, Tongshan, Xuzhou221116, China Jiangsu Provincial Key Laboratory of Educational Big Data Science and Engineering, Jiangsu Normal University, 101 Shanghai Road, Tongshan, Xuzhou221116, China E-mail: liupengfei@jsnu.edu.cn
Xuejun Ma
Affiliation:
School of Mathematical Sciences, Soochow University, 1 Shizi Street, Suzhou215006, China E-mail: xuejunma@suda.edu.cn
Wang Zhou
Affiliation:
Department of Statistics and Applied Probability, National University of Singapore, 6 Science Drive 2, Singapore117546, Singapore E-mail: stazw@nus.edu.sg
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Abstract

We construct a high-order conditional distance covariance, which generalizes the notation of conditional distance covariance. The joint conditional distance covariance is defined as a linear combination of conditional distance covariances, which can capture the joint relation of many random vectors given one vector. Furthermore, we develop a new method of conditional independence test based on the joint conditional distance covariance. Simulation results indicate that the proposed method is very effective. We also apply our method to analyze the relationships of PM2.5 in five Chinese cities: Beijing, Tianjin, Jinan, Tangshan and Qinhuangdao by the Gaussian graphical model.

Keywords

conditional distance covarianceconditional mutual independencelocal bootstrap
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 1 , January 2022 , pp. 126 - 143
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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