On the rate of convergence of estimate of the unknown distribution function of the first order autoregression process
type: Item
instance of: scholarly article
zbMATH Open document ID: 0970.62057
author: K. B. Selyakov
publication date: 2001-09-11T00:00:00Z
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 62G20
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62G05
zbMATH DE Number: 1645071
zbMATH Keywords: first order autoregression
zbMATH Keywords: distribution function
zbMATH Keywords: estimate
zbMATH Keywords: rate of convergence
MaRDI profile type: Publication
title: On the rate of convergence of estimate of the unknown distribution function of the first order autoregression process
published in: Visnyk Donets'kogo Universytetu. Seriya A. Pryrodnychi Nauky
review text: Let observations of the autoregressive series \(U_k=\beta U_{k-1}+\varepsilon_k,\;k=l,\dots,n,\) be given, where \(\beta\) is an unknown nonrandom parameter and \(\varepsilon_k\) are independent, identically distributed random variables with zero mean, finite variance and unknown distribution function \(G(x)\). Let \(\hat G(x)\) be the standard estimate of \(G(x)\). The author proposes an exponential estimate from below for the probability \(P\{\sup_x\sqrt{n}|\hat{G}(x)- G(x)|>\varepsilon\}\).
reviewed by: M. P. Moklyachuk
description: scientific article; zbMATH DE number 1645071