Seemingly Unrelated Ridge Regression in Semiparametric Models

Abstract

Abstract This article is concerned with the problem of multicollinearity in the linear part of a seemingly unrelated semiparametric (SUS) model. It is also suspected that some additional non stochastic linear constraints hold on the whole parameter space. In the sequel, we propose semiparametric ridge and non ridge type estimators combining the restricted least squares methods 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 asymptotic distributional properties are derived. Also, necessary and sufficient conditions for the superiority of the ridge-type estimator over the non ridge type estimator for selecting the ridge parameter K are derived. Lastly, a Monte Carlo simulation study is conducted to estimate the parametric and nonparametric parts. In this regard, kernel smoothing and cross validation methods for estimating the nonparametric function are used. Keywords: Feasible ridge estimatorKernel smoothingLinear restrictionsMulticollinearitySeemingly unrelated semiparametric modelMathematics Subject Classification: Primary 62G08Secondary 62J05, 62J07 Acknowledgment We are grateful to thank the anonymous referees for their constructing comments which significantly improved the presentation of the article.