An application of shrinkage estimation to the nonlinear regression model

Various large sample estimation techniques in a nonlinear regression model are presented. These estimators are based around preliminary tests of significance, and the James–Stein rule. The properties of these estimators are studied when estimating regression coefficients in the multiple nonlinear regression model when it is a priori suspected that the coefficients may be restricted to a subspace. A simulation based on a demand for money model shows the superiority of the positive-part shrinkage estimator, in terms of standard measures of asymptotic distributional quadratic bias and risk measures, over a range of economically meaningful parameter values. Further work remains in analysing the use of these estimators in economic applications, relative to the inferential approach which is best to use in these circumstances.