Authors

• Mahdi Roozbeh ¹
• Mohammad Arash ²
• Gholam Kibria ³

¹ Department of Statistics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Iran.

² Department of Statistics, School of Mathematical Sciences, University of Shahrood, Iran.

³ Department of Mathematics and Statistics, Florida International University, Florida, USA.

Abstract

In the context of ridge regression, the estimation of ridge (shrinkage) parameter plays an important role in analyzing data. Many efforts have been put to develop skills and methods of computing shrinkage estimators for different full-parametric ridge regression approaches, using eigenvalues. However, the estimation of shrinkage parameter is neglected for semiparametric regression models. The main focus of this paper is to develop necessary tools for computing the risk function of regression coefficient based on the eigenvalues of design matrix in semiparametric regression model, making use of differencing methodology. In this respect, some new estimators for shrinkage parameter are also proposed. It is shown that one of these estimators which is constructed based on well-known harmonic mean, performs better for large values of signal to noise ratio. For our proposal, the Monte Carlo simulation studies and a real application related to housing attributes are conducted to illustrate the efficiency of shrinkage estimators based on minimum risk criteria.

Keywords

• Differencing methodology
• Generalized ridge estimator
• kernel smoothing
• multicollinearity
• semiparametric regression model