Hidden Markov model likelihoods and their derivatives behave like i.i.d. ones

Peter J. Bickel, Ya'acov Ritov and Tobias Rydén

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,

ISSN 1403-9338
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 Petrie's (1969).
Key words:
Hidden Markov model, incomplete data, missing data, asymptotic normality