New Ridge Regression Estimator in Semiparametric Regression Models

In the context of ridge regression, the estimation of shrinkage parameter plays an important role in analyzing data. Many efforts have been put to develop the computation of risk function in different full-parametric ridge regression approaches using eigenvalues and then bringing an efficient estimator of shrinkage parameter based on them. In this respect, the estimation of shrinkage parameter is neglected for semiparametric regression model. Not restricted, but the main focus of this approach is to develop necessary tools for computing the risk function of regression coefficient based on the eigenvalues of design matrix in semiparametric regression. For this purpose the differencing methodology is applied. We also propose a new estimator for shrinkage parameter which is of harmonic type mean of ridge estimators. It is shown that this estimator performs better than all the existing ones for the regression coefficient. For our proposal, a Monte Carlo simulation study and a real dataset analysis related to housing attributes are conducted to illustrate the efficiency of shrinkage estimators based on the minimum risk and mean squared error criteria.