B0917
Title: Stein's method for estimation purposes
Authors: Adrian Fischer - Université libre de Bruxelles (Belgium) [presenting]
Robert Gaunt - The University of Manchester (United Kingdom)
Bruno Ebner - Karlsruhe Institute of Technology (Germany)
Yvik Swan - Universite libre de Bruxelles (Belgium)
Babette Picker - Karlsruhe Institute of Technology (Germany)
Abstract: In Stein's method, one can characterize probability distributions with differential operators. These characterizations are used to obtain a new class of point estimators for marginal parameters of strictly stationary and ergodic processes. These so-called Stein estimators satisfy the desirable classical properties such as consistency and asymptotic normality. As a consequence of the usually simple form of the operator, explicit estimators are obtained in cases where standard methods such as (pseudo-)maximum likelihood estimation (MLE) require a numerical procedure to calculate the estimate. In addition, with the approach, one can choose from a large class of test functions which allows to improve significantly on the moment estimator. For several probability laws, an estimator can be determined that shows an asymptotic behaviour close to efficiency in the i.i.d. case. Moreover, for i.i.d. observations, data-dependent functions are retrieved that result in asymptotically efficient estimators and a sequence of explicit Stein estimators is given that converge to the MLE.
