Assessing the Relative Performance of Penalty and Non-penalty Estimators in a Partially Linear Model

We investigated the linear shrinkage and shrinkage pretest estimators in a partially linear model, when it is a priori suspected that the regression coefficient may be restricted to a subspace. Using Monte Carlo simulations, we compared their performance with those of some penalty estimators. The proposed estimators were more efficient than the penalty estimators when the number of non-significant predictors was large. The shrinkage pretest estimator is suggested for practical applications, since its performance was robust against the reliability of the restriction. The proposed estimators were also applied to a real dataset to confirm their practicality.