Robustness estimators of location:a classification of linear and adaptive estimators

Abstract

Real-world data sets may be described in terms similar to trauma cases- ‘messy’ with ‘high morbidity’. Alternative estimators to the traditional mean are examined via a simulation study over a wide range of both symmetric and asymmetric distributions. These alternative estimators are data depenmdent and, in most cases, represent data far better than the usual mean. Princeton and post-Princeton linear and adaptive estimators of location are summarized, and a classification scheme based on an ancillary or selector statistic is proposed. The computational formulae for the collection of estimators have been standardized, as have the ancillary statistics. We classify these estimators by their computational form, give the computational formulae for each in a standardized notation, evaluate the subclass of estimators, and identify our ‘winner’ in that class.