A computational strategy for doubly smoothed MLE exemplified in the normal mixture model

Authors:
Byungtae Seo;Bruce G. Lindsay
Affiliations:
Department of Mathematics and Statistics, Texas Tech University, Broadway and Boston, Lubbock, TX 79409, USA;Department of Statistics, Pennsylvania State University, 326 Thomas building, University Park, PA 16802, USA
Venue:
Computational Statistics & Data Analysis
Year:
2010

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Abstract

A typical problem for the parameter estimation in normal mixture models is an unbounded likelihood and the presence of many spurious local maxima. To resolve this problem, we apply the doubly smoothed maximum likelihood estimator (DS-MLE) proposed by Seo and Lindsay (in preparation). We discuss the computational issues of the DS-MLE and propose a simulation-based DS-MLE using Monte Carlo methods as a general computational tool. Simulation results show that the DS-MLE is virtually consistent for any bandwidth choice. Moreover, the parameter estimates in the DS-MLE are quite robust to the choice of bandwidths, as the theory indicates. A new method for the bandwidth selection is also proposed.