Preliminary test and estimation in some multifactor diffusion processes

Abstract

We consider the general inference problem of the drift parameters matrices of m independent multivariate diffusion processes. In particular, we develop preliminary test and Stein-type estimation theory for m-parameters matrices which are suspected to satisfy some constraints. By using asymptotic distributional quadratic risk criterion, we analyze the relative performance of the pretest and shrinkage estimators. Further, we generalize some inference problems recently studied for a single multifactor Vasicek model. Finally, we carry out some simulation studies whose results corroborate our theoretical findings for observation periods of small and moderate lengths of time.