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

Abstract

Measures of φ-divergences are widely used as statistical tools for making inferences about a collection p1, p2, ..., pM 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 φ-divergence are 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.