ON MINIMUM DISTANCE ESTIMATION IN RECURRENT MARKOV STEP PROCESSES II

R. HÖPFNER^{1} AND YU. A. KUTOYANTS^{2}

1Institut für Mathematische Stochastik, Universität Freiburg, Hebelstrasse 27, D-79104 Freiburg im Breisgau, Germany 2Laboratoire de Statistique et Processus, Universite du Maine, F-72085 Le Mans, Cédex 9, France

(Received May 8, 1996; revised June 10, 1997)

Abstract. Consider a Markov step process X = (X_{t})_{t≥0} whose generator depends on an unknown parameter ϑ. We are interested in estimation of ϑ by a class of minimum distance estimators (MDE) based on observation of X up to time S_{n}, with (S_{n})_{n} a sequence of stopping times increasing to ∞. We give a precise description of the MDE error at stage n, for n fixed, i.e. a stochastic expansion in terms of powers of a norming constant and suitable coefficients (which can be calculated explicitly from the observed path of X up to time S_{n}).

Key words and phrases: Markov step processes, minimum distance estimators, stochastic expansions.