Asymptotics of Least Trimmed Squares Regression

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 thoroughly studied (from the robustness point of view) high breakdown-point estimators. In spite of its increasing popularity and number of applications, there are only conjectures and hints about its asymptotic behavior in regression after two decades of its existence. We derive here all important asymptotic properties of LTS, including the asymptotic normality and variance, under mild beta-mixing conditions