Qualitative robustness for stochastic processes
type: Item
instance of: scholarly article
title: Qualitative robustness for stochastic processes
zbMATH Open document ID: 0644.62037
author: Graciela Boente
author: Ricardo Fraiman
author: Victor J. Yohai
published in: The Annals of Statistics
publication date: 1987-01-01T00:00:00Z
review text: Defining appropriate metrics between samples, the authors generalize Hampel's concept of qualitative robustness of a sequence of estimators (\(\pi\)-robustness) to the case of stochastic processes. Also a new approach to qualitative robustness is presented, based on the intuitive concept of resistance, where instead of considering the insensitivity of estimates with respect to small changes in distribution of a process, the insensitivity corresponds to a given sample point \(x\in X^{\infty}\). Resulting concepts of (asymptotic) strong and weak resistance are then related to \(\pi\)-robustness. It is shown, in particular, that when a finite-dimensional parameter is estimated, then \(\pi\)-robustness is equivalent to the weak resistance. The authors also prove that a class of estimates which includes generalized M-estimates (GM-estimates) for linear models and autoregressive processes is strongly resistant.
Mathematics Subject Classification ID: 62F35
Mathematics Subject Classification ID: 62M10
zbMATH DE Number: 4050761
zbMATH Keywords: pi-robustness
zbMATH Keywords: strong resistance
zbMATH Keywords: qualitative robustness
zbMATH Keywords: weak resistance
zbMATH Keywords: generalized M-estimates
zbMATH Keywords: linear models
zbMATH Keywords: autoregressive processes
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176350506
OpenAlex ID: W2028553454
DOI: 10.1214/AOS/1176350506
description: scientific article; zbMATH DE number 4050761