Pathologies of some minimum distance estimators
type: Item
instance of: scholarly article
title: Pathologies of some minimum distance estimators
zbMATH Open document ID: 0684.62029
author: David Donoho
author: Richard C. Liu
published in: The Annals of Statistics
publication date: 1988-01-01T00:00:00Z
review text: Asymptotic properties of minimum distance (MD) estimators are studied at the normal N(\(\theta\),1) model. In contrast with good stability properties of MD functionals the estimators are shown to exhibit sometimes pathological behaviour at distributions arbitrarily close to the model. The asymptotic variance of minimum Kolmogorov-Smirnov and Lévy distance estimators can be as large as desired while inconsistency occurs with Prokhorov and variation distances. Regularity of MD estimators is however present when Hilbertian distances are applied, like Cramér-von Mises and Hellinger. The functionals induced by these metrics are shown to be also Fréchet differentiable.
Mathematics Subject Classification ID: 62F35
Mathematics Subject Classification ID: 62F12
zbMATH DE Number: 4121219
zbMATH Keywords: minimum distance estimates
zbMATH Keywords: inconsistency
zbMATH Keywords: Fréchet differentiability of statistical functionals
zbMATH Keywords: Hadamard differentiability
zbMATH Keywords: stability properties
zbMATH Keywords: Kolmogorov-Smirnov
zbMATH Keywords: Lévy distance estimators
zbMATH Keywords: variation distances
zbMATH Keywords: Regularity of MD estimators
zbMATH Keywords: Hilbertian distances
zbMATH Keywords: Cramér- von Mises
zbMATH Keywords: Hellinger
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176350821
OpenAlex ID: W2006228748
DOI: 10.1214/AOS/1176350821
description: scientific article; zbMATH DE number 4121219