Local mixture models of exponential families

Details Local mixture models of exponential families Local mixture models of exponential families

2007-09-04

arxiv.org/abs/0709.0447v1

Bernoulli 2007, Vol. 13, No. 3, 623-640

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.3150/07-BEJ6170 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statist

Scientific paper

10.3150/07-BEJ6170

Exponential families are the workhorses of parametric modelling theory. One reason for their popularity is their associated inference theory, which is very clean, both from a theoretical and a computational point of view. One way in which this set of tools can be enriched in a natural and interpretable way is through mixing. This paper develops and applies the idea of local mixture modelling to exponential families. It shows that the highly interpretable and flexible models which result have enough structure to retain the attractive inferential properties of exponential families. In particular, results on identification, parameter orthogonality and log-concavity of the likelihood are proved.

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