An alternative regularity condition for Hájek's representation theorem
type: Item
instance of: scholarly article
title: An alternative regularity condition for Hájek's representation theorem
zbMATH Open document ID: 0611.62013
author: Luke Tierney
published in: The Annals of Statistics
publication date: 1987-01-01T00:00:00Z
review text: Hájek's representation theorem [\textit{J. Hájek}, Z. Wahrscheinlichkeitstheor. Verw. Geb. 14, 323-330 (1970; Zbl 0193.180)] 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.
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 62G05
zbMATH DE Number: 3988451
zbMATH Keywords: alternative regularity condition
zbMATH Keywords: regular estimators
zbMATH Keywords: continuous limit condition
zbMATH Keywords: weak convergence
zbMATH Keywords: Hájek's representation theorem
zbMATH Keywords: asymptotic efficiency
zbMATH Keywords: asymptotic information
zbMATH Keywords: limiting distribution
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176350277
OpenAlex ID: W1974740359
DOI: 10.1214/AOS/1176350277
description: scientific article; zbMATH DE number 3988451