A1498
Title: Least trimmed squares: Nuisance parameter free asymptotics
Authors: Bent Nielsen - University of Oxford (United Kingdom) [presenting]
Vanessa Berenguer Rico - University of Oxford (United Kingdom)
Abstract: 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 $\epsilon$-contamination model, shows that the asymptotic behavior of both regression and scale estimators depends on nuisance parameters. Using a recently proposed new model, in which the LTS estimator is maximum likelihood, it is shown 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.
