Predictive performance of linear regression models

In this paper, the cross-validation methods namely the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$C_{p}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>C</mi> <mi>p</mi> </msub> </math> </EquationSource> </InlineEquation>, PRESS and GCV are presented under the multiple linear regression model when multicollinearity exists and additional information imposes restrictions among the parameters that should hold in exact terms. The selection of the biasing parameters are given so as to minimize the cross-validation methods. An example is given which illustrates the comprehensive predictive assessment of various estimators and shows the usefullness of computing. Besides, the performance of the estimators under several different conditions is examined via a simulation study. The results displayed that the biased estimator versions and the restricted form of the biased estimator versions of cross-validation methods give better predictive performance in the presence of multicollinearity. Copyright Springer-Verlag Berlin Heidelberg 2015