Premium
Finite Sample Properties of the Maximum Likelihood Estimator and of Likelihood Ratio Tests in Hidden Markov Models
Author(s) -
Michalek S.,
Wagner M.,
Timmer J.,
Vach W.
Publication year - 2001
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/1521-4036(200111)43:7<863::aid-bimj863>3.0.co;2-s
Subject(s) - mathematics , estimator , statistics , likelihood ratio test , likelihood function , markov chain , markov model , sample size determination , restricted maximum likelihood , maximum likelihood
Abstract Hidden Markov models were successfully applied in various fields of time series analysis, especially for analyzing ion channel recordings. The maximum likelihood estimator (MLE) has recently been proven to be asymptotically normally distributed. Here, we investigate finite sample properties of the MLE and of different types of likelihood ratio tests (LRTs) by means of simulation studies. The MLE is shown to reach the asymptotic behavior within sample sizes that are common for various applications. Thus, reliable estimates and confidence intervals can be obtained. We give an approximative scaling function for the estimation error for finite samples, and investigate the power of different LRTs suitable for applications to ion channels, including tests for superimposed hidden Markov processes. Our results are applied to physiological sodium channel data.