Efficient Estimation in Markov Chain Models: An Introduction
University of Siegen, Siegen, Germany outline the theory of efficient estimation for semiparametric Markov chain models, and illustrate in a number of simple cases how the theory · 1999
Our approach requires the model to be &s;locally asymptotically normal&s;. In Sec. 2 we introduce this concept for general Markov chain models with possibly infinite-dimensional parameter and illustrate it with a few simple examples. In Sec. 3 we consider the problem of estimating a onedimensional function of the parameter and determine an optimal estimator within a simple class of estimators: the &s;asymptotically linear&s; and &s;regular&s; ones. Section 4 considers martingale estimating equations and indicates when they lead to asymptotically linear and regular estimators. Section 5 shows that the optimal asymptotically linear and regular estimator is already &s;efficient&s;, i.e., optimal among all regular estimators. The presentation is rigorous in Sections 2, 3 and 5, and heuristic in the others.