For a general class of unipolar, rotationally symmetric distributions on the multi-dimensional unit spherical surface, a characterization of locally best rotation-invariant test statistics is exploited in the construction of locally best rotation-invariant rank tests for modal location. Allied...

There are hypothesis testing problems for (nonlinear) functions of parameters against functional ordered alternatives for which a reduction to a conventional order-restricted hypothesis testing problem may not be feasible. While such problems can be handled in an asymptotic setup, among the...

For multinormal distributions, testing against a global shift alternative, the Hotelling T2-test is uniformly most powerful invariant, and hence admissible. For testing against restricted alternatives this feature may no longer be true. It is shown that whenever the dispersion matrix is an...

A general class of optimal and distribution-free rank tests for the two-sample modal directions problem on (hyper-) spheres is proposed, along with an asymptotic distribution theory for such spherical rank tests. The asymptotic optimality of the spherical rank tests in terms of power-equivalence...

The estimation of the covariance matrix or the multivariate components of variance is considered in the multivariate linear regression models with effects being fixed or random. In this paper, we propose a new method to show that usual unbiased estimators are improved on by the truncated...

For a multinormal distribution with an unknown dispersion matrix, union-intersection (UI) tests for the mean against one-sided alternatives are considered. The null distribution of the UI test statistic is derived and its power monotonicity properties are studied. A Stain-type two-stage...