On Minimum Distance Estimation in Recurrent Markov Step Processes. I
Reinhard Höpfner, Yury A. Kutoyants · Scandinavian Journal of Statistics · 1997
Consider a Markov step process X=(Xt)t≥0whose generator depends on an unknown d‐dimensional parameter ϑ. We look at certain empirical measures for recurrent Markov step processes and their a.s. convergence; based on this, we introduce a class of minimum distance estimators. For broad families of sequential observation schemes (at stage n, the trajectory of X is observed up to time Sn, (Sn)n a sequence of stopping times increasing to ∞), we formulate a stochastic expansion of the suitably rescaled estimation error; for a particular scheme, asymptotic normality is obtained as n→∞. A minimax property under misspecification of the model (in the sense that the true probability law is contiguous to the parametric model but not contained in it) is given.