Abstract:

The least trimmed squares (LTS) estimator is a robust regression estimator, which is known to be robust to bad leverage and many other types of outliers. Implementation of LTS requires choosing the number of `good' observations, which is generally unknown. In this paper, we propose consistent estimators for the proportion of `good' observations. The starting point is that when the number of `good' observations is known, the LTS estimator is maximum likelihood in the semi-parametric LTS model where `good' observations are normal and `outliers' are more extreme than `good' observations.  When the number of `good' observations is unknown, the proposed estimator must select one model among many non-nested semi-parametric models. We also show that the LTS estimator evaluated at the estimated proportion of `good' observations leads to standard, nuisance-parameter free inference.

Coordinators: Mikkel Sølvsten and Morten Ørregaard Nielsen