Premium
Parameter Estimation in Pair‐hidden Markov Models
Author(s) -
ARRIBASGIL ANA,
GASSIAT ELISABETH,
MATIAS CATHERINE
Publication year - 2006
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.1467-9469.2006.00513.x
Subject(s) - mathematics , divergence (linguistics) , markov property , parametrization (atmospheric modeling) , markov chain , parameter space , estimation theory , hidden markov model , consistency (knowledge bases) , formalism (music) , property (philosophy) , statistical physics , markov process , variable order markov model , markov model , statistics , computer science , artificial intelligence , discrete mathematics , art , musical , philosophy , linguistics , physics , epistemology , quantum mechanics , visual arts , radiative transfer
. This paper deals with parameter estimation in pair‐hidden Markov models. We first provide a rigorous formalism for these models and discuss possible definitions of likelihoods. The model is biologically motivated and therefore naturally leads to restrictions on the parameter space. Existence of two different information divergence rates is established and a divergence property is shown under additional assumptions. This yields consistency for the parameter in parametrization schemes for which the divergence property holds. Simulations illustrate different cases which are not covered by our results.