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## A PROJECTIVE APPROACH TO CONDITIONAL INDEPENDENCE TEST FOR DEPENDENT PROCESSES

Ê±¼ä£º2019-05-09

Statistics Seminar (2019-10)

Topic: A PROJECTIVE APPROACH TO  CONDITIONAL INDEPENDENCE TEST FOR DEPENDENT PROCESSES

Speaker: Liping Zhu, Renmin University of China

Time: Thursday, May 16, 14:00-15:00

Place: Room 217, Guanghua Building 2

Abstract:

Conditional independence is a fundamental concept in many scientific fields. In this paper, we propose a projective approach to measuring and testing  departure from conditional independence for dependent processes. Through projecting  high dimensional dependent processes onto low dimensional subspaces,  our proposed projective approach is  insensitive to the dimensions of the processes. We show that, under the common  $\beta$-mixing conditions, our proposed projective test  is $n$-consistent if these processes are conditionally independent  and root-$n$-consistent  otherwise.   We suggest a bootstrap procedure to approximate the asymptotic null distribution of the test statistic. The consistency of this bootstrap procedure is also rigorously established. The finite-sample performance of our proposed projective test is demonstrated through  simulations against various alternatives and an economic application to test Granger causality.

Introduction:

Liping Zhu received  PhD from East China Normal University in 2006. He is now a full professor in Institute of Statistics and Big Data, Renmin University of China. His present research interests are in high dimensional data analysis, semiparametric modelling, sufficient dimension reduction and variable selection, etc.

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