An Adaptive Multivariate Signed-Rank Test For The One-Sample Location Problem

A multivariate affine-invariant adaptive test procedure is proposed for the one-sample location problem. The procedure suggested uses the multivariate sign test based on interdirections suggested by Randles, a multivariate signed-rank procedure suggested by Peters and Randles, and a light-tailed version of the signed-rank procedure. A selection statistic constructed from univariate Mahalanobis distances is used to choose the appropriate sign or signed-rank procedure yielding a large sample test which performs well for a broad class of distributions. The performance of the adaptive procedure is assessed via Monte Carlo simulation results.