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December, 1987 Consistent Estimation of the Influence Function of Locally Asymptotically Linear Estimators
Chris A. J. Klaassen
Ann. Statist. 15(4): 1548-1562 (December, 1987). DOI: 10.1214/aos/1176350609


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.


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Chris A. J. Klaassen. "Consistent Estimation of the Influence Function of Locally Asymptotically Linear Estimators." Ann. Statist. 15 (4) 1548 - 1562, December, 1987.


Published: December, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0629.62041
MathSciNet: MR913573
Digital Object Identifier: 10.1214/aos/1176350609

Primary: 62G05
Secondary: 62F12, 62F35

Rights: Copyright © 1987 Institute of Mathematical Statistics


Vol.15 • No. 4 • December, 1987
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