Optimal non-diagonal-type estimators in linear regression under the prediction error sum of squares criterion

摘要

This article considers the notion of the non-diagonal-type estimator (NDTE) under the prediction error sum of squares (PRESS) criterion. First, the optimal NDTE in the PRESS sense is derived theoretically and applied to the cosmetics sales data. Second, we make a further study to extend the NDTE to the general case of the covariance matrix of the model and then give a Bayesian explanation for this extension. Third, two remarks concerned with some potential shortcomings of the NDTE are presented and an alternative solution is provided and illustrated by means of simulations.