Analysis of a Robust Variant of the Weighted Mean

• Activity Number: 182
• Type: Contributed
• Date/Time: Tuesday, August 13, 2002 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section*
• Author(s): James Yen*+
• Affiliation(s): National Institute of Standards & Technology
• Keywords: trimmed mean ; L-statistic ; empirical function

Abstract

In many situations, weighted means can achieve much lower variances than unweighted means by placing more weight on those observations that are more precise. However, that weighted means can be dominated by one or two observations with very large weights raises questions about their robustness. A robust variant of the weighted mean, by trimming portions of the weights off of either end, retains much of the precision of weighted means while adding robustness. We present asymptotic results based on the theory of weighted empirical functions, including a Central Limit­type theorem, estimates of variance, and procedures for forming confidence intervals. Finally, these procedures are demonstrated and tested using Monte Carlo studies.