Tests of hypotheses for and against order restrictions on multinomial parameters based on phi-divergences

Abstract

Measures of phi-divergences are widely used as statistical tools for making inferences about a collection p(1), p(2),...,p(M) of multinomial parameters (Morales et al. (1995), Zografos et al. (1990), etc). Many such collections appearing in practice exhibit a trend (Robertson (1978), Lee (1987), Robertson et al. (1988) and many others cited there). In this paper tests based on measures of phi-divergence arc considered for testing a. simple null hypothesis on a. collection of multinomial parameters against an order restricted alternative and for testing an order restriction against no restriction on the collection of multinomial parameters.