Variance Estimation of Maximum Composite Likelihood Estimator Under Hidden Markov Models

• Activity Number: 559
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 2:00 PM to 3:50 PM
• Sponsor: International Chinese Statistical Association
• Author(s): Yi Huang*+ and Jiahua Chen
• Companies: University of British Columbia and University of British Columbia
• Keywords: variance estimation ; composite likelihood ; hidden Markov models ; bootstrap

Abstract

Variance estimation is always hard for full likelihood approach under hidden Markov models. It is mainly due to the fact that the asymptotic variance of maximum likelihood estimator admits a highly conceptual analytic form. By switching to the proposed composite likelihood approach, we derive a maximum composite likelihood estimator (MCLE) whose asymptotic variance has a simple and manageable expression. The asymptotic variance of MCLE is so simple that a plug-in estimator is available at once. We also propose a moving block bootstrap (MBB) method for the variance estimation. When the true parameter is an interior point of the parameter space, the usual MBB method, where the bootstrap sample is as large as the original, produces a consistent estimator of the asymptotic variance. The conclusion is not true when the true parameter is on the boundary. We have found that if the bootstrap sample is much smaller than the original sample then this obstacle can be resolved.