Shrinkage estimation in nonlinear regression The Box-Cox transformation

Abstract

The risk superiority of the Stein-rule estimator over the maximum likelihood (ML) estimator is known in the context of the normal linear regression model. We present a positive-part Stein-like estimator that dominates the ML and pretest estimators under quadratic loss, weighted by the information matrix, in nonlinear regression. The risk properties of ML, constrained ML, pretest, and shrinkage estimators for the Box-Cox model are discussed. In a Monte Carlo experiment, the shrinkage estimator dominates the ML estimator under the unweighted quadratic loss. However, the ML estimator may have lower risk than the shrinkage estimator under other weighted quadratic loss functions in small samples.