Application of a robustness measure for parameter estimation

The application of a novel approach to robust parameter estimation is investigated. As opposed to schemes based on classical saddlepoint techniques, this new approach is based on geometric concepts. An advantage to this method is that quantitative measures of robustness, which can be applied to finite sample and/or asymptotic studies, for a particular estimator can be obtained. These robustness measures are used to compare the robustness and performance characteristics of three location estimation schemes for the case where the data are modeled by independent and nominally identically distributed Laplace random variables. The three estimators studied are the sample mean, the sample median, and a censored sample mean estimate