S0246-0203(02)01134-2/FLA HIDDEN MARKOV MODEL LIKELIHOODS AND THEIR DERIVATIVES BEHAVE LIKE I.I.D. ONES✩

ABSTRACT. – We consider the log-likelihood function of hidden Markov models, its derivatives and expectations of these (such as different information functions). We give explicit expressions for these functions and bound them as the size of the chain increases. We apply our bounds to obtain partial second order asymptotics and some qualitative properties of a special model as well as to extend some results of [19]. 2002 Éditions scientifiques et médicales Elsevier SAS MSC: 62M0