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Biometrika 1982 69(1):145-151; doi:10.1093/biomet/69.1.145
© 1982 by Biometrika Trust
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Some unimodality properties of likelihoods derived from grouped data

J. BURRIDGE

Management Science and Business Studies Division, British Telecom London

This paper considers unimodality properties of certain likelihoods derived from grouped data. Three main types of model are considered: exponential families, linear models and empirical Bayes models. Partial answers are offered to questions raised in recent papers and areas needing further clarification are indicated. The paper shows that a link between the models is a theorem given by Prekopa on strongly unimodal probability densities and indicates ways of using the theorem to formulate models for analysing grouped multimodal univariate data.

Key Words: Concave function • Empirical Bayes • Exponential family • Grouped data • Linear model • Maximum likelihood • Strong unimodality


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