Semiparametric Ridge Regression Approach in Partially Linear Models

Abstract

In this article, we introduce a semiparametric ridge regression estimator for the vector-parameter in a partial linear model. It is also assumed that some additional artificial linear restrictions are imposed to the whole parameter space and the errors are dependent. This estimator is a generalization of the well-known restricted least-squares estimator and is confined to the (affine) subspace which is generated by the restrictions. Asymptotic distributional bias and risk are also derived and the comparison result is then given.

Keywords:

• Asymptotic distributional risk
• Kernel smoothing
• Linear restrictions
• Ridge regression estimator
• Semiparametric least squares

Acknowledgments

We are grateful to thank the anonymous referee for his/her constructing comments which significantly improved the presentation of the article. The partial support from the Ordered and Spatial Data Center of Excellence, Ferdowsi University of Mashhad, Iran is also acknowledged.