Moderate and Cramér-type large deviation theorems for M-estimators
type: Item
instance of: scholarly article
title: Moderate and Cramér-type large deviation theorems for M-estimators
zbMATH Open document ID: 0638.62032
DOI: 10.1016/0167-7152(88)90119-8
author: Wilbert C. M. Kallenberg
author: Jana Jurečková
author: Noël Veraverbeke
published in: Statistics \& Probability Letters
publication date: 1988-01-01T00:00:00Z
full work available at URL: moderate-and-cramertype-large-deviation-theorems-for-mestimators(0f75cd05-0a8a-4191-a4ec-5a11d3575497).html
review text: Let \(X_ 1,...,X_ n\) be i.i.d. r.v.'s. Let \(\{T_ n\}\) be a sequence of M-estimators of a parameter \(t_ 0\). For various type M-estimators the authors obtained sufficient conditions which assure either that for each \(\{\xi_ n\}\) with \(\lim \epsilon_ n=0\) and \(\lim n \epsilon_ n=\infty\), \[ -\lim_{n\to \infty}(n \epsilon^ 2_ n)^{-1} \log P(| T_ n-t_ 0| >\epsilon_ n)=(2\sigma^ 2)^{-1} \] or that uniformly in the range \(-c\leq x\leq o(n^{1/6})\) \((c\geq 0)\) \[ P((T_ n-t_ 0)n^{1/2} \sigma^{-1}>x)=\{1-\Phi (x)\}(1+o(1))\quad (n\to \infty). \]
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 4041050
zbMATH Keywords: central limit result
zbMATH Keywords: location
zbMATH Keywords: scale
zbMATH Keywords: moderate deviations
zbMATH Keywords: Cramér type large deviations
zbMATH Keywords: inaccuracy rate
zbMATH Keywords: asymptotic variance
zbMATH Keywords: M-estimators
zbMATH Keywords: sufficient conditions
reviewed by: Ken-ichi Yoshihara
MaRDI profile type: Publication
OpenAlex ID: W2146945588
cites work: Robust Statistics
cites work: Q3753275
cites work: Q5525725
cites work: Q4085018
cites work: Q5568451
cites work: Q3857500
description: scientific article; zbMATH DE number 4041050