On the rate of convergence of empirical distribution functions in \(AR(1)\) models
type: Item
instance of: scholarly article
zbMATH Open document ID: 0971.62025
author: K. B. Selyakov
publication date: 2001-09-16T00:00:00Z
Mathematics Subject Classification ID: 62G20
Mathematics Subject Classification ID: 62G30
Mathematics Subject Classification ID: 62M10
zbMATH DE Number: 1646310
zbMATH Keywords: residual distribution
zbMATH Keywords: autoregression
zbMATH Keywords: nonparametric estimation
zbMATH Keywords: uniform confidence intervals
MaRDI profile type: Publication
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title: On the rate of convergence of empirical distribution functions in \(AR(1)\) models
published in: Prykladna Statystyka. Aktuarna ta Finansova Matematyka
review text: The author considers an \(AR(1)\) process \(U_k=\beta U_{k-1}+\varepsilon_k\), where \(\varepsilon_k\) are i.i.d. with d.f. \(G\). The unknown \(G\) is estimated by the empirical distribution function of the residuals \(G_n\). The author derives an upper bound for NEWLINE\[NEWLINE\Pr\{\sup_x\sqrt{n}|G_n(x)-G(x)|>\varepsilon\},NEWLINE\]NEWLINE for the case when NEWLINE\[NEWLINE\sup_x|G''(x)|<\infty,\quad E\varepsilon_n^4<\infty,\quad |\beta|\leq\Lambda<1.NEWLINE\]
description: scientific article; zbMATH DE number 1646310