ABSTRACT

Much of statistics is concerned with parameter estimation. Perhaps the most common estimation problems are those of location and scale estimation in single samples. The sample mean and standard deviation, which are the best location and scale estimates under the strict assumption of normality, are known to be poor robust estimates under even slight departures from the normal distribution; in fact, in their evaluation of the robustness of 68 univariate estimates of location, Andrews et al. (1972) state:

"Which was the worst estimator in the study? If there is any clear candidate for such an overall statement, it is the arithmetic mean, long celebrated because of its many "optimality properties" and its revered use in applications. There is no contradiction: the optimality questions of mathematical theory are important for that theory and very useful, as orientation points, for applicable procedures. If taken as anything more than that, they are completely irrelevant and misleading for the broad requirements of practice."