TITLE: Efficient Robust Estimation via Two-Stage Generalized Empirical Likelihood

SPEAKER: Dr. Howard Bondell

ABSTRACT:

The triumvirate of outlier resistance, distributional robustness, and
efficiency in both small and large samples, constitute the Holy Grail
of robust statistics. We show that a two-stage procedure based on
an initial robust estimate of scale followed by an application of
generalized empirical likelihood comes very close to attaining that goal.
The resulting estimators are able to attain full asymptotic efficiency at
the Normal distribution, while simulations point to the ability to
maintain this efficiency down to small sample sizes. Additionally, the
estimators are shown to have the maximum attainable finite-sample
replacement
breakdown point, and thus remain stable in the presence of heavy-tailed
distributions and outliers. Although previous proposals with full
asymptotic efficiency exist in the literature, their finite sample
efficiency can often be low. The method is discussed in detail
for linear regression, but can be naturally extended to other areas,
such as multivariate estimation of location and covariance.