In this paper, we study a class of two sample test statistics based on inter-point distances in the high dimensional and low/medium size setting. Our include well-known energy distance maximum mean discrepancy with Gaussian Laplacian kernels, critical values are obtained via permutations. We show that all these tests inconsistent when distributions correspond to same marginal but differ other a...

Abstract Yang et al. proved that the symmetric random walk Metropolis–Hastings algorithm for Bayesian variable selection is rapidly mixing under mild high-dimensional assumptions. We propose a novel Markov chain Monte Carlo (MCMC) sampler using an informed proposal scheme, which we prove achieves much faster time independent of number covariates, assumptions To best our knowledge, this first re...

Estimation and hypothesis tests for the covariance matrix in high dimensions is a challenging problem as traditional multivariate asymptotic theory no longer valid. When dimension larger than or increasing with sample size, standard likelihood based have poor performance. Existing dimensional are either computationally expensive very weak control of type I error. In this paper, we propose test ...