The consistency of the least trimmed squares estimator (see Rousseeuw \cite{Rous} or Hampel et al. \cite{HamRonRouSta}) is proved under general conditions. The assumptions employed in paper are discussed in details to clarify the consequences for the applications.
n−−√-consistency of the least trimmed squares estimator is proved under general conditions. The proof is based on deriving the asymptotic linearity of normal equations.
Asymptotic normality of the least trimmed squares estimator is proved under general conditions. At the end of paper a discussion of applicability of the estimator (including the discussion of algorithm for its evaluation) is offered.