R-Estimates vs. GMM: A Theoretical Case Study of Validity and Efficiency

Loading...
Thumbnail Image
Penn collection
Statistics Papers
Degree type
Discipline
Subject
attributable effects
efficiency robustness
generalized method of moments
group rank test
Hodges–Lehmann estimate
MERT
permutation test
Statistics and Probability
Funder
Grant number
License
Copyright date
Distributor
Related resources
Author
Small, Dylan S
Gastwirth, Joseph L
Krieger, Abba M
Rosenbaum, Paul R
Contributor
Abstract

What role should assumptions play in inference? We present a small theoretical case study of a simple, clean case, namely the nonparametric comparison of two continuous distributions using (essentially) information about quartiles, that is, the central information displayed in a pair of boxplots. In particular, we contrast a suggestion of John Tukey—that the validity of inferences should not depend on assumptions, but assumptions have a role in efficiency—with a competing suggestion that is an aspect of Hansen’s generalized method of moments—that methods should achieve maximum asymptotic efficiency with fewer assumptions. In our case study, the practical performance of these two suggestions is strikingly different. An aspect of this comparison concerns the unification or separation of the tasks of estimation assuming a model and testing the fit of that model. We also look at a method (MERT) that aims not at best performance, but rather at achieving reasonable performance across a set of plausible models.

Advisor
Date Range for Data Collection (Start Date)
Date Range for Data Collection (End Date)
Digital Object Identifier
Series name and number
Publication date
2006-01-01
Journal title
Statistical Science
Volume number
Issue number
Publisher
Publisher DOI
Journal Issue
Comments
Recommended citation
Collection