Inefficient Best Invariant Tests
Abstract
Test statistics which are invariant under various subgroups of the orthogonal group are shown to provide tests whose powers are asymptotically equal to their level against the usual type of contiguous alternative in models where the number of parameters is allowed to grow as the sample size increases. The result is applied to the usual analysis of variance test in the Neyman-Scott many means problem and to an analogous problem in exponential families. Proofs are based on a method used by Cibisov(1961) to study spacings statistics in a goodness-of-fit problem. We review the scope of the technique in this context.
Cite
@article{arxiv.1608.05994,
title = {Inefficient Best Invariant Tests},
author = {Richard A Lockhart},
journal= {arXiv preprint arXiv:1608.05994},
year = {2016}
}
Comments
Originally written in 1992. Savagely reviewed (say I) at the Annals and I lacked the courage to submit it anywhere else. It is, though, limit law in models with many parameters and so may have some relevance today, I feel