Least trimmed squares in nonlinear regression under dependence

Abstract

High breakdown-point regression estimators protect against large errors both in explanatory and dependent variables. The least trimmed squares (LTS) estimator is one of frequently used, easily understandable and, from the robustness point of view, thoroughly studied high breakdown-point estimators. In spite of its increasing popularity and a number of applications, very little is known about its asymptotic behaviour in nonlinear, panel-data, and time-series regression after two decades of its existence. In this context, we derive and discuss all important asymptotic properties of LTS, including the asymptotic normality and variance, under mild β -mixing conditions.