Powerful Invariant Test Research Articles

Optimum Invariant Tests in Unbalanced Variance Components Models

In this paper the problem of testing the hypothesis $\Delta \leqq \Delta_0$ against $\Delta > \Delta_0$, where $\Delta$ is the ratio of variances in the one-way classification of the analysis of variance with variance components, is treated. The model is not restricted to equal class frequencies. It is found that the most powerful invariant test against an alternative $\Delta_1$ depends upon $\Delta_1$, but has the property of maximising the minimum power over the set of alternatives with $\Delta \geqq \Delta_1$. The test statistic is distributed like a ratio of linear combinations of independent chi-square distributed random variables. It is shown that a statistic used by Wald [6] to derive a confidence interval for $\Delta$ gives a test that is almost equal to the most powerful invariant tests against large alternatives $\Delta_1$. For the case $\Delta_0 = 0$ it is equal to the usual test in the fixed-effects model. In the balanced case the test reduces to the usual $F$-test which Herbach [2] has proved to be both uniformly most powerful invariant and uniformly most powerful unbiased.

Hypothesis Testing of Gaussian Processes with Composite Alternatives

This paper is concerned with the problems of making statistical inferences on stochastic processes. It will be restricted to the case, of white Gaussian processes. The object of this paper is to determine a hypothesis testing procedure for a simple hypothesis versus a composite alternative. Investigations are carried out here for the case where the domain of the stochastic parameter is the unit circle. Composite alternatives are handled by considering only those tests which remain invariant under the group of rotations for the unit circle. The paper will consist of two parts. Part I will be of concern when only one sample function of the process is tested. In this case besides the uniformly most powerful invariant test, the Bayes solution and the test based on the least favorable distribution are also found. In Part II the sequential counterpart of Part I is considered. Here the best invariant test is found.