Leave-K-Out Likelihood: Alternative for Selecting the Best Likelihood-Based Estimator in the Presence of Multiple Local Maximizers

• Activity Number: 184
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Daeyoung Kim*+ and Byungtae Seo
• Companies: University of Massachusetts Amherst and Department of Statistics, Sungkyunkwan University
• Keywords: Likelihood ; Multiple local maximizer ; Spurious local maximizer ; Mixture model

Abstract

There are a type of mixture models for which the likelihood equations may have multiple roots corresponding to local maximizers of the likelihood even if the global maximum likelihood estimator is inconsistent or does not even exist. In these cases the likelihood theory often guarantees the existence of a consistent and efficient root, but in general may not provide a method to easily select an appropriate likelihood root in practice. In this paper we propose using the leave-$k$-out likelihood designed to select a statistically desirable (theoretically consistent and practically non-spurious) local maximizer when the global maximizer is unavailable or unsuitable for parameter estimate and the multiple local maximizers are present. The performance of the proposed method is illustrated on some examples, a few of which are published in the literature.