Title: Efficiency in the high-dimensional one-sample location problem
Authors: Davy Paindaveine - Universite libre de Bruxelles (Belgium) [presenting]
Thomas Verdebout - Universite Libre de Bruxelles (Belgium)
Abstract: The one-sample location testing problem is considered in a high-dimensional setup where the dimension $p$ goes to infinity with the sample size $n$. We consider two types of problems, according to whether the direction of the possible shift is specified or not. Under a sphericity assumption, we investigate the null and non-null asymptotic distributions of two natural tests, namely the (spherical version of) the Hotelling test and the spatial sign test. Our results show in particular that these two tests share the same local asymptotic powers under power-exponential distributions, but not under t distributions. Also, the local alternatives that can be detected by both tests may depend on the underlying distribution, which is highly non-standard. We further partly read our results in terms of contiguity and local asymptotic normality. Throughout, we conduct Monte Carlo experiments to illustrate the finite-sample relevance of the results.