Least Trimmed Squares for Regression Models with Stable Errors

Abstract

Least Trimmed Squares (LTS) is a robust regression method with respect to outliers. It is based on performing Ordinary Least Squares (OLS) estimates on sub-datasets and determining the optimal solution corresponding to the minimum sum of squared residuals. Since the method of LTS is based on OLS, errors in regression models have finite variance. This work aims to generalize LTS for heavy tail data with infinite variance. When errors have infinite variance, it is impossible to benefit from OLS estimates. We use the property of variance existence of most ordered errors to find an initial robust OLS estimate. We polish the LTS method with a maximum likelihood estimator based on the density function of order statistics and determine the optimal solution for stable regression models. The proposed algorithm is implemented for linear regression models.