Hinge estimators of location: Robust to asymmetry

Abstract

Robust estimators have been developed and tested for symmetric distributions via simulation studies. The primary objective of these robust estimators was to show that these estimators had a higher efficiency than the sample mean over these symmetric distributions. Little attention has been given to how these estimators perform on data that are from asymmetric distributions or from distributions that have inherent anomalies-so called ‘messy data’. This study is intended to supplement previous 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 available. In the asymmetric data distributions faced on a daily basis, estimators that adapt themselves to the data may be formulated and used. We recommend the use of the following algorithm in examining data sets: (a) compute the ancillary statisticsskewness and tail-length to classify the data distribution; (b) analyze each data set using at least one alternative estimator to the usual XM; (c) if the results are similar, report the XM analysis; (d) if the results are dissimilar, report the alternative analysis and the reasons for using the alternative analysis (i.e., t-tests based on a Tα, HQ 1, HQ 2, or SK5).