The Small-Sample Efficiency of Some Recently Proposed Multivariate Measures of Location

Abstract

Numerous multivariate robust measures of location have been proposed and many have been found to be unsatisfactory in terms of their small-sample efficiency. Several new measures of location have recently been derived, however, nothing is known about their small-sample efficiency or how they compare to the sample mean under normality. This research compared the efficiency for p = 2, 5, and 8 with sample sizes n = 20 and 50 for p-variate data. Although previous studies indicate that so-called skipped estimators are efficient, this study found that variations of this approach can perform poorly when n is small and p exceeds 5. One of the best estimators was found to be a skipped estimator where outliers detected by a projection method are eliminated. The TBS, OGK and RMBA estimators were included and; in some cases, they performed well, however, serious exceptions were identified suggesting that a skipped estimator based on a projection-type outlier detection method is preferable based on efficiency.