Report：Projection correlation between two random vectors

Time：10:00am Oct13,2017
Place：Room104,Building of Statistics of School
Reporter：Runze Li， Verne M. Willaman Professor of Statistics，The Pennsylvania State University

  Homepage: http://www.personal.psu.edu/ril4/

Abstract：We propose projection correlation  to characterize  dependence between two random vectors. Projection correlation has several appealing properties. Specifically, it  equals zero if and only if the two random vectors are independent; it  is not sensitive to the dimensions of the two random vectors; and it is  invariant with respect to the group of orthogonal transformations; and  its estimation is free of tuning parameters and does not require  moment conditions on the random vectors. We show that the  sample estimate of the projection correction   is n-consistent if the two random vectors are independent and root-n-consistent otherwise. Monte Carlo simulation studies indicate that the projection correlation   has higher power than both the distance correlation  and the ranks of distances in  tests of independence, especially when the dimensions  are  relatively large or the moment conditions required by the distance correlation  are violated.