Robustness to Spurious Observations of Linearized Hodges-Lehmann Estimators and Anscombe Estimators

Some recent literature has been devoted to the discussion of estimation of parameters in the presence of spurious observations, that is, observations generated from a source not intended. When this type of contamination is feared, estimators that guard against this possibility are desired, and once defined, their performance, measured by their premiums and protections, is of interest. In this paper, two types of estimators that have been proposed for this type of situation, the Hodges-Lehmann linearized estimators and Anscombe estimators, are discussed when sampling is thought to be from N(θ, σ2). but spuriousness may occur of the mean shift type N(θ + A, σ2). Comparisons of the rules are made through a Monte Carlo study of the premium and protection of these rules.