Hybrid principal component regression estimation in linear regression

In this paper, the principal component regression (PCR) estimators for regression parameters were studied in a linear regression model. After discussing the advantages and disadvantages of the classical PCR, we put forward three versions of hybrid PCR estimators. For the first two versions, we obtained the corresponding optimal solutions under the prediction error sum of squares (PRESS) criterion, while for the last one we offered two methods for obtaining the solution. In order to examine their practicality and generalizability, we considered two real-world examples and conducted a simulation study, which took into account varying degrees of multicollinearity. The numerical experiment revealed that the new estimators could substantially improve the least squares (LS) and classical PCR estimators under the PRESS criterion.