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Likelihood Ratio Testing for Hidden Markov Models Under Non‐standard Conditions
Author(s) -
DANNEMANN JÖRN,
HOLZMANN HAJO
Publication year - 2008
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2007.00587.x
Subject(s) - mathematics , markov chain , likelihood ratio test , independent and identically distributed random variables , stochastic matrix , parametric statistics , hidden markov model , boundary (topology) , markov model , statistics , random variable , artificial intelligence , computer science , mathematical analysis
. In practical applications, when testing parametric restrictions for hidden Markov models (HMMs), one frequently encounters non‐standard situations such as testing for zero entries in the transition matrix, one‐sided tests for the parameters of the transition matrix or for the components of the stationary distribution of the underlying Markov chain, or testing boundary restrictions on the parameters of the state‐dependent distributions. In this paper, we briefly discuss how the relevant asymptotic distribution theory for the likelihood ratio test (LRT) when the true parameter is on the boundary extends from the independent and identically distributed situation to HMMs. Then we concentrate on discussing a number of relevant examples. The finite‐sample performance of the LRT in such situations is investigated in a simulation study. An application to series of epileptic seizure counts concludes the paper.