Some statistical implications of multivariate inequality constrained testing

Abstract

Within the context of a linear statistical model and multivariate inequality constrained testing, this paper is concerned with i) the statistical implications that flow from the case of two joint one-sided tests and ii) the use of the resulting pre-test risk functions in making decisions concerning the choice between these tests in practice. The informational content of the pre-test criteria, for the particular testing problem at hand, is discussed and, under a squared error loss measure, the unfavorable sampling performances of inequality pre-test estimators are noted.

Keywords:

• inequality constrained testing
• joint one-sided tests
• pre-test estimator
• power of the test
• squared error loss