Least Trimmed Squares Asymptotics: Regression with leverage

Abstract:

Least Trimmed Squares (LTS) regression is known to be robust to ‘outliers’ and in particular to bad leverage points. However, the current asymptotic theory for LTS is of limited use as its assumptions rule out leverage and the asymptotic distribution depends on the unknown contamination. We use a new model, where ‘outlier’ errors are extreme relative to the ‘good’ errors and where leverage effects are possible. We show that in this model the LTS estimator has an asymptotic distribution that is free of nuisance parameters. Thus, with the new model standard inference procedures apply while allowing a broad range of contamination.