Development and Comparison of M-Estimators for Location on the Basis of the Asymptotic Variance Functional.
Abstract
A new approach for comparison and modification of M-estimators is introduced and implemented. The problem considered is that of robust estimation of a location parameter. Specific attention is given to the epsilon-contaminated normal model. The analytical method introduced is based upon the asymptotic variance of the estimator, the asymptotic variance being considered as a functional over the space of distribution functions. The behavior of this functional is investigated with respect to special sub-families within a neighborhood of the 'central' distribution. With respect to the normal location problem, three robust estimators from the 1972 Princeton Monte Carlo study are examined: the 'Huber' H15, the 'Hampel' 25A, and the sine function M-estimator AMT. Using the asymptotic variance functional analysis as both an analytical and intuitive tool, three modified estimators are suggested and developed. All six estimators are then compared at selected distributions heavier tailed than the normal. Besides its analytical and intuitive appeal, this functional approach offers a cost-saving alternative to Monte Carlo Methods. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1976
- Accession Number
- ADA042680
Entities
People
- Dennis D. Boos
- Robert Serfling
Organizations
- Florida State University