The Annals of Statistics

An Alternative Regularity Condition for Hajek's Representation Theorem

Luke Tierney

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Abstract

Hajek's representation theorem states that under certain regularity conditions the limiting distribution of an estimator can be written as the convolution of a certain normal distribution with some other distribution. This result, originally developed for finite dimensional problems, has been extended to a number of infinite dimensional settings where it has been used, for example, to establish the asymptotic efficiency of the Kaplan-Meier estimator. The purpose of this note is to show that the somewhat unintuitive regularity condition on the estimators that is usually used can be replaced by a simple one: It is sufficient for the asymptotic information and the limiting distribution of the estimator to vary continuously with the parameter being estimated.

Article information

Source
Ann. Statist., Volume 15, Number 1 (1987), 427-431.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350277

Digital Object Identifier
doi:10.1214/aos/1176350277

Mathematical Reviews number (MathSciNet)
MR885748

Zentralblatt MATH identifier
0611.62013

JSTOR
links.jstor.org

Subjects
Primary: 62G20: Asymptotic properties
Secondary: 62G05: Estimation

Keywords
Asymptotic efficiency regular estimators

Citation

Tierney, Luke. An Alternative Regularity Condition for Hajek's Representation Theorem. Ann. Statist. 15 (1987), no. 1, 427--431. doi:10.1214/aos/1176350277. https://projecteuclid.org/euclid.aos/1176350277


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See also

  • Acknowledgment of Prior Result: Luke Tierney. Acknowledgement of Priority: An Alternative Regularity Condition for Hajek's Representation Theorem. Ann. Statist., vol. 16, no. 2 (1988), 926.