Shrinkage strategies in some multiple multi-factor dynamical systems

University of Windsor, 401 Sunset Avenue, Windsor, N9B 3P4, Ontario, Canada
severien@uwindsor.ca

Received: 10 July 2009
Revised: 27 February 2010

Abstract

In this paper, we are interested in estimation problem for the drift parameters matrices of m independent multivariate diffusion processes. More specifically, we consider the case where the m-parameters matrices are supposed to satisfy some uncertain constraints. Given such an uncertainty, we develop shrinkage estimators which improve over the performance of the maximum likelihood estimator (MLE). Under an asymptotic distributional quadratic risk criterion, we study the relative dominance of the established estimators. Further, we carry out simulation studies for observation periods of small and moderate lengths of time that corroborate the theoretical finding for which shrinkage estimators outperform over the MLE. The proposed method is useful in model assessment and variable selection.