Constructing tests for normal order-restricted inference. (English) Zbl 0837.62050

Cohen, Arthur; Sackrowitz, Harold B.; Samuel-Cahn, Ester

Bernoulli 1, No. 4, 321-333 (1995).

Summary: For normal models we consider the problem of testing a null hypothesis against an order-restricted alternative. The alternative always consists of a cone minus the null space. We offer sufficient conditions for a class of tests to be complete and for unbiasedness of tests. Both sets of sufficient conditions are expressed in terms of the notion of cone order monotonicity. A method of constructing tests that are unbiased and in the complete class is given. The method yields new tests of value to many problems. Detailed applications and a simulation study are offered for testing homogeneity of means against the simple order alternative and for testing homogeneity against the matrix order alternative.

MSC:

62H15	Hypothesis testing in multivariate analysis
62F30	Parametric inference under constraints
62C07	Complete class results in statistical decision theory

Keywords:

Bayes-type tests; cone ordering; convexity; dual cone; likelihood ratio test; normal models; order-restricted alternative; unbiasedness; sufficient conditions; cone order monotonicity; simulation study; testing homogeneity of means; simple order alternative; matrix order alternative