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ON MINIMUM DISTANCE ESTIMATION IN RECURRENT

MARKOV STEP PROCESSES II

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

^{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* = (*X*_{t})_{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 *S*_{n}, with (*S*_{n})_{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 *S*_{n}).

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

**Source**
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