HINGE ESTIMATORS OF LOCATION - ROBUST TO ASYMMETRY

Robust estimators have been developed and tested for symmetric distrib utions via simulation studies. The primary objective of these robust e stimators was to show that these estimators had a higher efficiency th an the sample mean over these symmetric distributions. Little attentio n has been given to how these estimators perform on data that are from asymmetric distributions or from distributions that have inherent ano malies-so called 'messy data'. This study is intended to supplement pr evious studies by examining the behavior of several robust estimators over asymmetric distributions. The objective is to demonstrate several adaptive 'asymmetric' robust estimators which utilize sample selector statistics to identify the underlying distribution and to demonstrate the efficiency of these adaptive estimators. From a methodology point rather than a theoretical basis, reasonable alternatives should be av ailable. In the asymmetric data distributions faced on a daily basis, estimators that adapt themselves to the data may be formulated and use d. We recommend the use of the following algorithm in examining data s ets: (a) compute the ancillary statistics-skewness and tail-length to classify the data distribution; (b) analyze each data set using at lea st one alternative estimator to the usual XM; (c) if the results are s imilar, report the XM analysis; (d) if the results are dissimilar, rep ort the alternative analysis and the reasons for using the alternative analysis (i.e. t-tests based on a T alpha, HQ(1), HQ(2), or SK5).