Abstract
Consider the loglinear model for categorical data under the assumption of either Poisson, multinomial, or product-multinomial sampling. We are interested in testing between various hypotheses on the parameter space. In this paper, the usual likelihood ratio test, with maximum likelihood estimators for the unspecified parameters, is generalized to tests based on φ-divergences, still using maximum likelihood estimators. These tests yield the likelihood ratio test as a special case. Asymptotic distributions for the new test statistics are derived under both the null and the alternative hypotheses. Then it is shown how the φ-divergences can be used to test nested hypotheses, yielding a type of “analysis of divergence”.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.