The Least Trimmed Squares (LTS) regression estimator is known to be very
robust to the presence of ‘outliers’. It is based on a clear and intuitive idea: in a
sample of size n, it searches for the h-subsample of observations with the smallest
sum of squared residuals. The remaining n−h observations are declared ‘outliers’.
Fast algorithms for its computation exist. Nevertheless, the existing asymptotic
theory for LTS, based on the traditional ϵ-contamination model, shows that the
asymptotic behavior of both regression and scale estimators depend on nuisance
parameters. Using a recently proposed new model, in which the LTS estimator
is maximum likelihood, we show that the asymptotic behavior of both the LTS
regression and scale estimators are free of nuisance parameters. Thus, with the
new model as a benchmark, standard inference procedures apply while allowing a
broad range of contamination.
