Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-27T07:40:45.203Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Xuejun Ma
Affiliation:
School of Mathematical Sciences, Soochow University, 1 Shizi Street, Suzhou215006, China E-mail: [email protected]
Wang Zhou
Affiliation:
Department of Statistics and Applied Probability, National University of Singapore, 6 Science Drive 2, Singapore117546, Singapore E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bowman, A.W. (1984). An alternative method of cross-validation for the smoothing of density estimates. Biometrika 71(2): 353–360.CrossRefGoogle Scholar
Chacon, J.E. & Duong, T. (2010). Multivariate plug-in bandwidth selection with unconstrained pilot bandwidth matrices. Test 19(2): 375–398.CrossRefGoogle Scholar
Chakraborty, S. & Zhang, X. (2018). Distance metrics for measuring joint dependence with application to causal inference. Journal of the American Statistical Association 114(528): 1638–1650.CrossRefGoogle Scholar
Duong, T. & Hazelton, M.L. (2005). Cross-validation bandwidth matrices for multivariate kernel density estimation. Scandinavian Journal of Statistics 32(3): 485–506.CrossRefGoogle Scholar
Edwards, D (2012). Introduction to graphical modelling. New York: Springer.Google Scholar
Huang, T.M. (2010). Testing conditional independence using maximal nonlinear conditional correlation. The Annals of Statistics 38(4): 2047–2091.CrossRefGoogle Scholar
Linton, O. & Gozalo, P. (2014). Testing conditional independence restrictions. Econometric Reviews 33(5–6): 523–552.CrossRefGoogle Scholar
Scutari, M. (2009). Learning Bayesian networks with the bnlearn R package. Journal of Statistical Software 35(3): 1–22.Google Scholar
Su, L. & White, H. (2014). Testing conditional independence via empirical likelihood. Journal of Econometrics 182(1): 27–44.CrossRefGoogle Scholar
Szekely, G.J., Rizzo, M.L., & Bakirov, N.K. (2007). Measuring and testing dependence by correlation of distances. The Annals of Statistics 35(6): 2769–2794.CrossRefGoogle Scholar
Wand, M.P. & Jones, M.C. (1994). Multivariate plug-in bandwidth selection. Computational Statistics 9(2): 97–116.Google Scholar
Wang, X., Pan, W., Hu, W., Tian, Y., & Zhang, H. (2015). Conditional distance correlation. Journal of the American Statistical Association 110(512): 1726–1734.CrossRefGoogle ScholarPubMed