We study theproblem ofnonparametric dependence detection. Many existing methods maysuffer severepower loss due to non-uniform consistency, which we illustratewith a paradox.To avoid such power loss, we approach the nonparametric testof independencethrough the new framework of binary expansion statistics(BEStat) and binaryexpansion testing (BET), which examine dependence through anovel binaryexpansion filtration approximation of the copula. Through aHadamard transform,we find that the symmetry statistics in the filtration arecomplete sufficientstatistics for dependence. These statistics are alsouncorrelated under thenull. By utilizing symmetry statistics, the BET avoids theproblem ofnon-uniform consistency and improves upon a wide class ofcommonly used methods(a) by achieving the minimax rate in sample size requirementfor reliable powerand (b) by providing clear interpretations of globalrelationships uponrejection of independence. The binary expansion approach alsoconnects thesymmetry statistics with the current computing system tofacilitate efficientbitwise implementation. We illustrate the BET with a study ofthe distributionof stars in the night sky and with an exploratory dataanalysis of the TCGAbreast cancer data.
About the Speaker:
Dr. Kai Zhang is currently an associate professor with tenure at the Department of Statistics and Operations Research, UNC Chapel Hill. Dr. Zhang obtained his bachelor's degree from Peking University in 2003, his Ph.D. degree in mathematics from Temple University in 2007, and his Ph.D. degree in statistics from the Wharton School, University of Pennsylvania in 2012. His research interests include nonparametric statistics, high-dimensional statistics, and post-selection inference. His research is supported by three grants from the National Science Foundation of the United States.