ESAIM: Probability and Statistics

Table of Contents - 2012 - Volume 16  

Research Article

Shrinkage strategies in some multiple multi-factor dynamical systems

Sévérien Nkurunziza

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

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.

(Received July 10 2009)

(Revised February 27 2010)

(Online publication July 3 2012)

Key Words:

  • Asymptotic distributional risk;
  • diffusion process;
  • MLE;
  • Shrinkage estimator;
  • Wiener process.

Mathematics Subject Classification:

  • 62M05;
  • 58J65