Nonparametric estimation of the stationary waiting time distribution function for the \(GI/G/1\) queue
type: Item
instance of: scholarly article
title: Nonparametric estimation of the stationary waiting time distribution function for the \(GI/G/1\) queue
zbMATH Open document ID: 0824.60095
published in: The Annals of Statistics
publication date: 1995-10-31T00:00:00Z
review text: The stochastic model in question is regarded as a functional that relates a quantity of interest, here the waiting time distribution in a (the) standard queueing model, to certain input distributions for which natural estimators exist. The statistical properties of these estimators, such as consistency, asymptotic normality, efficiency and functioning of the bootstrap, are well understood, and it is shown here that these properties carry over to the natural estimator for the quantity of interest that results if the functional is applied to the input estimators. In order to make this work certain local analytic properties of the functional are established, notably continuity and differentiability with respect to a suitable norm. The paper combines probabilistic, analytical and statistical ideas and techniques.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 62G05
zbMATH DE Number: 756500
zbMATH Keywords: queue
zbMATH Keywords: nonparametric estimation
zbMATH Keywords: statistical properties
zbMATH Keywords: bootstrap
zbMATH Keywords: local analytic properties
zbMATH Keywords: statistical ideas and techniques
author: Susan M. Pitts
reviewed by: Rudolf Grübel
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176325635
OpenAlex ID: W1993008599
DOI: 10.1214/AOS/1176325635
description: scientific article; zbMATH DE number 756500