Outlier robust Horvitz-Thompson estimators - ARCHIVED

The Horvitz-Thompson estimator (HT-estimator) is not robust against outliers. Outliers in the population may increase its variance though it remains unbiased. The HT-estimator is expressed as a least squares functional to robustify it through M-estimators. An approximate variance of the robustified HT-estimator is derived using a kind of influence function for sampling and an estimator of this variance is developed. An adaptive method to choose an M-estimator leads to minimum estimated risk estimators. These estimators and robustified HT-estimators are often more efficient than the HT-estimator when outliers occur.