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
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.
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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