Comparison between the Locally Most Mean Power Unbiased and Rao's Tests in the Multiparameter Case

This paper makes an asymptotic comparison, up to the third order, between the locally most mean power unbiased (LMMPU) and Rao's tests in the multi-parameter case. The two tests are seen to have identical power up to second order. It is also seen that Rao's test, which is much simpler than the LMMPU test, is almost as good as the latter, in terms of third-order local average power, for small but reasonable test size, provided the statistical curvature of the model is not too large.