Likelihood Inference in Some Finite Mixture Models

Xiaohong Chen (), Maria Ponomareva and Elie Tamer
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Elie Tamer: Dept. of Economics, Northwestern University

No 1895, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: Parametric mixture models are commonly used in applied work, especially empirical economics, where these models are often employed to learn for example about the proportions of various types in a given population. This paper examines the inference question on the proportions (mixing probability) in a simple mixture model in the presence of nuisance parameters when sample size is large. It is well known that likelihood inference in mixture models is complicated due to 1) lack of point identification, and 2) parameters (for example, mixing probabilities) whose true value may lie on the boundary of the parameter space. These issues cause the profiled likelihood ratio (PLR) statistic to admit asymptotic limits that differ discontinuously depending on how the true density of the data approaches the regions of singularities where there is lack of point identification. This lack of uniformity in the asymptotic distribution suggests that confidence intervals based on pointwise asymptotic approximations might lead to faulty inferences. This paper examines this problem in details in a finite mixture model and provides possible fixes based on the parametric bootstrap. We examine the performance of this parametric bootstrap in Monte Carlo experiments and apply it to data from Beauty Contest experiments. We also examine small sample inferences and projection methods.

Keywords: Finite mixtures; Parametric bootstrap; Profiled likelihood ratio statistic; Partial identification; Parameter on the boundary (search for similar items in EconPapers)
Pages: 37 pages
Date: 2013-05
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (1)

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Related works:
Journal Article: Likelihood inference in some finite mixture models (2014)
Working Paper: Likelihood inference in some finite mixture models (2013)
Working Paper: Likelihood inference in some finite mixture models (2013)
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