Skip to main content Accessibility help
×
Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-23T05:20:11.479Z Has data issue: false hasContentIssue false

17 - On the So-Called “Huber Sandwich Estimator” and “Robust Standard Errors”

Published online by Cambridge University Press:  05 June 2012

David Collier
Affiliation:
University of California, Berkeley
Jasjeet S. Sekhon
Affiliation:
University of California, Berkeley
Philip B. Stark
Affiliation:
University of California, Berkeley
Get access

Summary

Abstract. The “Huber Sandwich Estimator” can be used to estimate the variance of the MLE when the underlying model is incorrect. If the model is nearly correct, so are the usual standard errors, and robustification is unlikely to help much. On the other hand, if the model is seriously in error, the sandwich may help on the variance side, but the parameters being estimated by the MLE are likely to be meaningless–except perhaps as descriptive statistics.

Introduction

This chapter gives an informal account of the so-called “Huber Sandwich Estimator,” for which Peter Huber is not to be blamed. We discuss the algorithm and mention some of the ways in which it is applied. Although the chapter is mainly expository, the theoretical framework outlined here may have some elements of novelty. In brief, under rather stringent conditions the algorithm can be used to estimate the variance of the MLE when the underlying model is incorrect. However, the algorithm ignores bias, which may be appreciable. Thus, results are liable to be misleading.

To begin the mathematical exposition, let i index observations whose values are yi. Let θ ∈ Rp be a p × 1 parameter vector. Let yfi (y|θ) be a positive density. If yi takes only the values 0 or 1, which is the chief case of interest here, then fi (0|θ) > 0, fi (1|θ) > 0, and fi (0|θ) + fi (0|θ) + fi (1|θ) = 1. Some examples involve real- or vector-valued yi, and the notation is set up in terms of integrals rather than sums.

Type
Chapter
Information
Statistical Models and Causal Inference
A Dialogue with the Social Sciences
, pp. 295 - 304
Publisher: Cambridge University Press
Print publication year: 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×