Generalized quantile processes
type: Item
instance of: scholarly article
title: Generalized quantile processes
zbMATH Open document ID: 0757.60012
author: John H. J. Einmahl
author: David M. Mason
published in: The Annals of Statistics
publication date: 1992-09-27T00:00:00Z
review text: A quantile function pertaining to a probability measure \(P\) defined on the Borel subsets of the \(d\)-dimensional Euclidean space is introduced. This quantile function depends on a subclass \(A\) of all Borel sets as well as a real-valued function \(\lambda\) defined on \(A\). Particular choices of \(A\) and \(\lambda\) yield quantile functions describing various features of \(P\). When the concept is applied to the empirical measure based on independent and identically distributed \(d\)-dimensional random vectors, one obtains generalizations of the well-known one-dimensional empirical quantile process. Functional limit theorems are proved for these generalized quantile processes. Several examples arising from appropriate choices of \(A\) and \(\lambda\) are also discussed.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62G30
zbMATH DE Number: 64518
zbMATH Keywords: quantile function
zbMATH Keywords: empirical quantile process
zbMATH Keywords: Functional limit theorems
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176348670
OpenAlex ID: W2086404575
DOI: 10.1214/AOS/1176348670
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description: scientific article; zbMATH DE number 64518