Robust ridge estimator in restricted semiparametric regression models

Abstract

In this paper, ridge and non-ridge type estimators and their robust forms are defined in the semiparametric regression model when the errors are dependent and some non-stochastic linear restrictions are imposed under a multicollinearity setting. In the context of ridge regression, the estimation of shrinkage parameter plays an important role in analyzing data. Another common problem in applied statistics is the presence of outliers in the data besides multicollinearity. In this respect, we propose some robust estimators for shrinkage parameter based on least trimmed squares (LTS) method. Given a set of n observations and the integer trimming parameter h≤n, the LTS estimator involves computing the hyperplane that minimizes the sum of the smallest h squared residuals. The LTS estimator is closely related to the well-known least median squares (LMS) estimator in which the objective is to minimize the median squared residual. Although LTS estimator has the advantage of being statistically more efficient than LMS estimator, the computational complexity of LTS is less understood than LMS. Here, we extract the robust estimators for linear and nonlinear parts of the model based on robust shrinkage estimators. It is shown that these estimators perform better than ordinary ridge estimator. For our proposal, via a Monté-Carlo simulation and a real data example, performance of the ridge type of robust estimators are compared with the classical ones in restricted semiparametric regression models.