The Annals of Statistics

A robust adjustment of the profile likelihood

James E. Stafford

Full-text: Open access

Abstract

Under mild misspecifications of model assumptions, maximum likelihood estimates often remain consistent and asymptotically normal. Asymptotic normality will often hold for the signed root of the likelihood ratio statistic and the score statistic as well. However, standard estimates of asymptotic variance are usually inconsistent. This occurs when Bartlett's second identity fails. In the manner of McCullagh and Tibshirani, a variance correction may be used to adjust the profile likelihood so this identity obtains. The resulting likelihood yields the robust versions of the signed root, Wald and score statistic suggested by Kent and Royall.

Assuming model correctness, asymptotic expansions for the first three cumulants of each robust statistic are derived. It is seen that bias and skewness are not severely affected by using a robust statistic. An invariant expression derived for the asymptotic relative efficiency of a robust method allows assessment in numerous examples considered. Even for moderately large sample sizes, losses in efficiency are significant, making the misuse of a robust variance estimate potentially costly. Computer algebra is used in many of the calculations reported in this paper.

Article information

Source
Ann. Statist., Volume 24, Number 1 (1996), 336-352.

Dates
First available in Project Euclid: 26 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1033066212

Digital Object Identifier
doi:10.1214/aos/1033066212

Mathematical Reviews number (MathSciNet)
MR1389893

Zentralblatt MATH identifier
0905.62027

Subjects
Primary: 62F35: Robustness and adaptive procedures 62F05: Asymptotic properties of tests

Keywords
Asymptotic relative efficiency Bartlett identities computer algebra cumulants profile likelihood robustness

Citation

Stafford, James E. A robust adjustment of the profile likelihood. Ann. Statist. 24 (1996), no. 1, 336--352. doi:10.1214/aos/1033066212. https://projecteuclid.org/euclid.aos/1033066212


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