Consistent estimation of the order for Markov and hidden Markov chains

摘要: Abstract : The structural parameters of many statistical models can be estimated by maximizing a penalized version the likelihood function. author uses this idea to construct strongly consistent estimators order for Markov Chain and Hidden models. specification penalty term requires precise information on rate growth maximized ratio. For models, he determines using Law Iterated Logarithm. finds an upper bound results from Information Theory. He gives sufficient conditions avoid overestimation underestimation order. Examples terms that generate also are given.