B1046
Title: Test of independence based on generalized distance correlation
Authors: Danna Zhang - University of California, San Diego (United States) [presenting]
Abstract: The fundamental statistical inference concerning the testing of independence between two random vectors is studied. Existing asymptotic theories for test statistics based on distance covariance can only apply to either low-dimensional or high-dimensional settings. A novel unified distributional theory of the sample generalized distance covariance is developed that works for random vectors of arbitrary dimensions. In particular, a non-asymptotic error bound on its Gaussian approximation is derived. Under fairly mild moment conditions, the asymptotic null distribution of the sample generalized distance covariance is shown to be distributed as a linear combination of independent and identically distributed chi-squared random variables. High dimensionality is also shown to be necessary for the null distribution to be asymptotically normal. To estimate the asymptotic null distribution practically, an innovative Half-Permutation procedure is proposed and the theoretical justification for its validity is provided. The exact asymptotic distribution of the resampling distribution is derived under general marginal moment conditions and the proposed procedure is shown to be asymptotically equivalent to the oracle procedure with known marginal distributions.
