A class of biased estimators based on QR decomposition

Multicollinearity among the explanatory variables is a serious problem in regression analysis. There are some classes of biased estimators for solving this problem in statistical literature. In these biased classes, estimation of the shrinkage parameter plays an important role in data analyzing. Using eigenvalue analysis, efforts have been made to develop skills and methods for computing risk function of the estimators in regression models. Here, we propose a modified estimator based on the QR decomposition for solving the multicolinearity problem of design matrix, which makes the data to be less distorted than the other methods. The exact risk expressions in addition to biases are derived for the proposed estimators. Also, some results demonstrating superiority of the QR-based estimator over ordinary least-squares estimator for selecting the shrinkage parameter are obtained. Finally, a Monté-Carlo simulation study and a real data application related to acetylene data are used to support our theoretical discussion.