Use of the Bootstrap in Robust Estimation of Location

Abstract

Robust measures of location may be used in estimation problems to help to mitigate the possible effects of outliers or asymmetry. A practical difficulty is how to determine reliable valid estimates of the precision of the corresponding sample estimates. Commonly, precision is expressed by means of standard errors or confidence intervals. Several data sets are used to make comparisons of the performance of standard errors and confidence intervals based on both asymptotic normal results and the bootstrap for a number of robust location measures, including trimmed means with a fixed trimming level and Huber's proposal 2. Bootstrap results and asymptotic results using a winsorized standard deviation are generally comparable, but there is a tendency for the precision to be overstated with the latter both for very small data sets and for Huber's proposal 2 with skewed data sets. In addition, precision with Huber's proposal 2 is found to be marginally superior to that with the corresponding trimmed mean in the presence of extreme outliers.