Affine invariant depth-based tests for the multivariate one-sample location problem

摘要

A multivariate affine invariant family of depth-based tests is proposed for the one-sample location problem. Suitable outlyingness functions which are formulated using depth functions are used to construct the proposed tests. The asymptotic null distribution and the asymptotic relative efficiency of the tests are discussed under the class of centrally and elliptically symmetric distributions, respectively. Furthermore, a conditional distribution-free property of the tests is shown. The performance of the proposed tests is evaluated using a Monte Carlo study as well as asymptotic relative efficiencies and is compared to that of several competitors. It is observed that such tests yield a better performance as compared to their competitors for a wide spectrum of alternatives.