### R. HÖPFNER1 AND YU. A. KUTOYANTS2

1 Institut für Mathematische Stochastik, Universität Freiburg,
Hebelstrasse 27, D-79104 Freiburg im Breisgau, Germany

2 Laboratoire 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 = (Xt)t >0 whose generator depends on an unknown parameter vartheta. We are interested in estimation of vartheta by a class of minimum distance estimators (MDE) based on observation of X up to time Sn, with (Sn)n a sequence of stopping times increasing to \infty. 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 Sn).

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

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