Showing papers by "Wolfgang Wefelmeyer published in 2001"
TL;DR: In this paper, a lower bound for the asymptotic variance of regular estimators is derived for discretely observed diffusions. But the authors do not consider the transition distribution of a Markov chain.
Abstract: If we have a parametric model for the invariant distribution of a Markov chain but cannot or do not want to use any information about the transition distribution (except, perhaps, that the chain is reversible) — what, then, is the best use we can make of the observations? We determine a lower bound for the asymptotic variance of regular estimators and show constructively that the bound is attainable. The results apply to discretely observed diffusions. AMS 1991 subject classifications. Primary 62G20, 62M05; secondary 62F12.
17 citations
01 Jan 2001
TL;DR: In this paper, a lower bound for the asymptotic variance of regular estimators is derived for discretely observed diffusions. But the authors do not consider the transition distribution of a Markov chain.
Abstract: If we have a parametric model for the invariant distribution of a Markov chain but cannot or do not want to use any information about the transition distribution (except, perhaps, that the chain is reversible) — what, then, is the best use we can make of the observations? We determine a lower bound for the asymptotic variance of regular estimators and show constructively that the bound is attainable. The results apply to discretely observed diffusions. AMS 1991 subject classifications. Primary 62G20, 62M05; secondary 62F12.
16 citations
TL;DR: In this article, the stationary law of one or two successive observations of an ergodic Markov chain is shown to satisfy a linear constraint, and it is shown that the best of these estimators is efficient.
13 citations
01 Jan 2001
TL;DR: In this article, the authors consider estimating a real-valued functional a(F) for known and unknown parameters, and calculate the influence function and the asymptotic variance of a functional.
Abstract: Consider a locally asymptotically normal semiparametric model with a real parameter ? and a possibly infinite-dimensional parameter F. We are interested in estimating a real-valued functional a(F). If a# estimates a(F) for known ?, and ? estimates d, then the plug-in estimator a$ estimates a(F) if ? is unknown. We show that a? is asymptotically linear and regular if ?# and ? are, and calculate the influence function and the asymptotic variance of a?. If a(F) can be estimated adaptively with respect to d, then a$ is efficient if ?# is efficient. If a(F) cannot be estimated adaptively, then for ?0 to be efficient, ? must also be efficient. We illustrate the results with stochastic process models, in particular with time series models, and discuss extensions of the results.
8 citations