Feasible Ridge Estimator in Seemingly Unrelated Semiparametric Models

Abstract

This article considers estimation in the seemingly unrelated semiparametric models, when the explanatory variables are affected by multicollinearity. It is also suspected that some additional linear constraints may hold on the whole parameter space. In sequel we propose difference-based ridge type estimators combining the restricted least squares method in the model under study. For practical aspects, it is assumed that the covariance matrix of error terms is unknown and thus feasible estimators are proposed and their biases and covariances are derived. Also, necessary and sufficient conditions for the superiority of the ridge type estimator over the nonridge type estimator for selecting the ridge parameter are derived. Lastly, a Monte Carlo simulation study is conducted to estimate the parametric and nonparametric parts. In this regard, local linear regression method for estimating the nonparametric function is used.

Keywords:

• Differencing estimator
• Feasible restricted least squares estimator
• Multicollinearity
• Ridge estimator
• Seemingly unrelated semiparametric model

Mathematics Subject Classification:

• Primary 62J05
• Secondary 62G08
• 62J07

Acknowledgment

The authors thank the anonymous referee for his/her helpful comments that let to vast improvement and putting many details in the paper.