Testing for homogeneity in mixture models

Jiaying Gu (jiaying.gu@utoronto.ca), Roger Koenker (rkoenker@uiuc.edu) and Stanislav Volgushev
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Jiaying Gu: Institute for Fiscal Studies and University of Toronto
Roger Koenker: Institute for Fiscal Studies and UCL
Stanislav Volgushev: Institute for Fiscal Studies

No CWP09/13, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: Statistical models of unobserved heterogeneity are typically formalised as mixtures of simple parametric models and interest naturally focuses on testing for homogeneity versus general mixture alternatives. Many tests of this type can be interpreted as C(a) tests, as in Neyman (1959), and shown to be locally, asymptotically optimal. A unified approach to analysing the asymptotic behaviour of such tests will be described, employing a variant of the LeCam LAN framework. These C(a) tests will be contrasted with a new approach to likelihood ratio testing for mixture models. The latter tests are based on estimation of general (nonparametric) mixture models using the Kiefer and Wolfowitz (1956) maximum likelihood method. Recent developments in convex optimisation are shown to dramatically improve upon earlier EM methods for computation of these estimators, and new results on the large sample behaviour of likelihood rations involving such estimators yield a tractable form of asymptotic inference. We compare performance of the two approaches identifying circumstances in which each is preferred.

Date: 2013-03-12
New Economics Papers: this item is included in nep-ecm
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