Extended least trimmed squares estimator in semiparametric regression models with correlated errors

Abstract

Under a semiparametric regression model, a family of robust estimates for the regression parameter is proposed. The least trimmed squares (LTS) method is a statistical technique for fitting a regression model to a set of points. 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 develop an algorithm for the LTS estimator. Through a Monte Carlo approach, performance of the robust estimates is compared with the classical ones in semiparametric regression models.