Asymptotic normality of the maximum likelihood estimate in Markov processes

Metrika ◽  
1969 ◽  
Vol 14 (1) ◽  
pp. 62-70 ◽  
Author(s):  
G. G. Roussas
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Normality ◽  
Markov Processes ◽  
Maximum Likelihood Estimate ◽  
Likelihood Estimate

scholarly journals Asymptotic normality of M-estimators in nonhomogeneous hidden Markov models

2011 ◽  
Vol 48 (A) ◽  
pp. 295-306
Author(s):  
Jens Ledet Jensen
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Normality ◽  
Hidden Markov Models ◽  
Maximum Likelihood Estimate ◽  
Markov Models ◽  
Hidden Markov ◽  
Likelihood Estimate ◽  
Mixing Properties ◽  
Dependent Variables ◽  
Hidden Markov Process

Results on asymptotic normality for the maximum likelihood estimate in hidden Markov models are extended in two directions. The stationarity assumption is relaxed, which allows for a covariate process influencing the hidden Markov process. Furthermore, a class of estimating equations is considered instead of the maximum likelihood estimate. The basic ingredients are mixing properties of the process and a general central limit theorem for weakly dependent variables.

scholarly journals Asymptotic normality of M-estimators in nonhomogeneous hidden Markov models

2011 ◽  
Vol 48 (A) ◽  
pp. 295-306 ◽  
Author(s):  
Jens Ledet Jensen
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Normality ◽  
Hidden Markov Models ◽  
Maximum Likelihood Estimate ◽  
Markov Models ◽  
Hidden Markov ◽  
Likelihood Estimate ◽  
Mixing Properties ◽  
Dependent Variables ◽  
Hidden Markov Process

Results on asymptotic normality for the maximum likelihood estimate in hidden Markov models are extended in two directions. The stationarity assumption is relaxed, which allows for a covariate process influencing the hidden Markov process. Furthermore, a class of estimating equations is considered instead of the maximum likelihood estimate. The basic ingredients are mixing properties of the process and a general central limit theorem for weakly dependent variables.

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