Feasible ridge estimator in partially linear models

In a partial linear model, some non-stochastic linear restrictions are imposed under a multicollinearity setting. Semiparametric ridge and non-ridge type estimators, in a restricted manifold are defined. For practical use, it is assumed that the covariance matrix of the error term is unknown and thus feasible estimators are replaced and their asymptotic distributional properties are derived. Also, necessary and sufficient conditions, for the superiority of the ridge type estimator over its counterpart, for selecting the ridge parameter k are obtained. Lastly, a Monte Carlo simulation study is conducted to estimate the parametric and non-parametric parts. In this regard, kernel smoothing and cross validation methods for estimating the non-parametric function are used.