TESTING INDEPENDENCE FOR HIGH DIMENSIONAL DATA WITH APPLICATION TO TIME SERIES

Gabor Szekely (pronounced say-kay)

Abstract:
Brownian distance correlation was introduced about six years ago by G.J. Szekely. This correlation characterizes independence and determines a consistent test of multivariate independence for random vectors in arbitrary dimension. In this talk a modified Brownian distance correlation is proposed and applied to the problem of testing independence of random vectors in high dimension. The distribution of a simple transformation of the test statistic converges to Student t as dimension tends to infinity for any fixed sample size. Thus we obtain a distance correlation t test for independence of random vectors in arbitrarily high dimension, applicable under very general conditions. One of the important applications is testing independence of two times series.

Background:
Székely attended the Eötvös Loránd University, Hungary graduating in 1970. His first advisor was Alfréd Rényi. Székely received his Ph.D. in 1971 from Eötvös Loránd University, the Candidate Degree in 1976 under the direction of Paul Erdös and Andrey Kolmogorov, and the Doctor of Science degree from the Hungarian Academy of Sciences in 1986. Between 1985 and 1995 Székely was the first program manager of the Budapest Semesters in Mathematics. Between 1990 and 1997 he was the founding chair of the Department of Stochastics of the Budapest Institute of Technology (Technical University of Budapest) and editor-in-chief of Matematikai Lapok, the official journal of the János Bolyai Mathematical Society. In 1989 Székely was visiting professor at Yale University, and in 1990-91 he was the first Lukacs Distinguished Professor in Ohio. Székely was academic advisor of Morgan Stanley, NY, and Bunge, Chicago, helped to establish the Morgan Stanley Mathematical Modeling Centre in Budapest (2005) and the Bunge Mathematical Institute (BMI) in Warsaw (2006) to provide quantitative analysis to support the firms' global business. Since 2006 he is a Program Director of Statistics of the National Science Foundation. Székely is also Research Fellow of the Rényi Institute of Mathematics of the Hungarian Academy of Sciences and the author of two monographs, Paradoxes of Probability Theory and Mathematical Statistics, and Algebraic Probability Theory (with Imre Z. Ruzsa).