Abstract
Consider a Markov step process X = (Xt)t≥0 whose generator depends on an unknown parameters ϑ. We are interested in estimation of ϑ 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 ∞. 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).
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Höpfner, R., Kutoyants, Y.A. On Minimum Distance Estimation in Recurrent Markov Step Processes II. Annals of the Institute of Statistical Mathematics 50, 493–502 (1998). https://doi.org/10.1023/A:1003525428320
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DOI: https://doi.org/10.1023/A:1003525428320