Discrimination distance bounds and statistical applications
type: Item
instance of: scholarly article
title: Discrimination distance bounds and statistical applications
zbMATH Open document ID: 0685.60040
DOI: 10.1007/BF01208258
author: Marek Kanter
publication date: 1990-01-01T00:00:00Z
review text: Bounds are obtained for the Kullback-Leibler discrimination distance between two random vectors X and Y. If X is a sequence of independent random variables whose densities have similar tail behavior and \(Y=AX\), where A is an invertible matrix, then the bounds are a product of terms depending on A and X separately. These bounds help indicate the best possible rate of convergence for any estimator of the parameters of an auto-regressive process with innovations in the domain of attraction of a stable law. We provide a general theorem establishing the link between total variation proximity of measures and the rate of convergence of statistical estimates to complete our argument.
Mathematics Subject Classification ID: 60G30
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 32M10
zbMATH DE Number: 4122967
zbMATH Keywords: Kullback-Leibler discrimination distance
zbMATH Keywords: tail behavior
zbMATH Keywords: rate of convergence
zbMATH Keywords: domain of attraction
zbMATH Keywords: stable law
MaRDI profile type: Publication
cites work: Asymptotic efficiency of statistical estimators: concepts and higher order asymptotic efficiency
cites work: Q3894827
cites work: Q3876829
cites work: Limit theory for the sample covariance and correlation functions of moving averages
cites work: Q3733431
cites work: Q3806622
cites work: Autoregressive processes with infinite variance
cites work: Regression and autoregression with infinite variance
cites work: Q3260839
cites work: Q3289112
cites work: Asymptotic methods in statistical decision theory
cites work: Q3272826
cites work: Contiguity of Probability Measures
cites work: On criteria for cn-consistency of estimators
full work available at URL: https://doi.org/10.1007/bf01208258
OpenAlex ID: W1990562626
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4122967