We describe a central limit theorem for a sum of random variables that can be approximated by weakly dependent variables, following the formulation in Goetze and Hipp (1983).

The result has applications to asymptotic results for nonhomogeneous hidden Markov processes (Jensen, 2011).

For a hidden Markov process the hidden variables, as well as the observed variables, are strongly mixing. However, when writing the log likelihood function as a sum each term typically depends on most of the observed variables.

In the talk the central limit theorem will be motivated by a number of hidden Markov models considered in the literature.

References:

Goetze, F. and Hipp, C. (1983): Asymptotic expansion for sums of weakly dependent random vectors. Z. Wahrsch. verw. Gebiete 64, 211-240.

Jens, J.L. (2011): Asymptotic normality of M-estimators in nonhomogeneous hidden Markov models. To appear in J. Appl. Prob. Spec. Vol. 48A.

Keywords: central limit theorem; nonhomogeneous hidden Markov; strongly mixing; asymptotic normality

Biography: Professor Jens Ledet Jensen has been employed by Aarhus University since 1982 and been a full professor from 1998. He has worked mainly in asymptotics, espicially with the use of saddlepoint approximations. In recent years he has turned towards bioinformatics and the use of hidden Markov Models.