Hypothesis testing in a generic nesting framework for general distributions

Nested parameter spaces, either in the null or alternative hypothesis, often enable an improvement in the performance of the tests. In this context, order restricted inference has not been studied in detail. Divergence based measures provide a flexible tool for proposing some useful test statistics, which usually contain the likelihood ratio-test statistics as a special case. The existing literature on hypothesis testing under inequality constraints, based on phi-divergence measures, is concentrated on specific models with multinomial sampling. In this paper the existing results are extended and unified through new families of test-statistics that are valid for nested parameter spaces containing either equality or inequality constraints and general distributions for either single or multiple populations.