The Annals of Statistics

Consistent Estimation of the Influence Function of Locally Asymptotically Linear Estimators

Chris A. J. Klaassen

Full-text: Open access

Abstract

Consider estimators which behave locally asymptotically like an average of some function taken at the observations. This function is called the influence function and one calls such estimators locally asymptotically linear. It is shown that the influence function of a locally asymptotically linear estimator can be estimated consistently and conversely, that, given a consistent estimator of the influence function, estimators can be constructed which are locally asymptotically linear in that influence function. With the help of these results an adaptive estimator is constructed for a partially irregular model.

Article information

Source
Ann. Statist., Volume 15, Number 4 (1987), 1548-1562.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350609

Digital Object Identifier
doi:10.1214/aos/1176350609

Mathematical Reviews number (MathSciNet)
MR913573

Zentralblatt MATH identifier
0629.62041

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62F12: Asymptotic properties of estimators 62F35: Robustness and adaptive procedures

Keywords
Influence function asymptotically linear estimators consistency adaptive estimation irregular model

Citation

Klaassen, Chris A. J. Consistent Estimation of the Influence Function of Locally Asymptotically Linear Estimators. Ann. Statist. 15 (1987), no. 4, 1548--1562. doi:10.1214/aos/1176350609. https://projecteuclid.org/euclid.aos/1176350609


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