Hadamard differentiability on \(D[0,1]^p\)
type: Item
instance of: scholarly article
title: Hadamard differentiability on \(D[0,1]^p\)
zbMATH Open document ID: 0898.62019
author: Jian-Jian Ren
author: Pranab K. Sen
published in: Journal of Multivariate Analysis
publication date: 1998-10-26T00:00:00Z
review text: The asymptotic normality of a statistical functional via the Hadamard derivative for univariate observations has been studied by \textit{J. A. Reeds} [On the definition of von Mises functionals. Ph.D. Diss., Harvard Univ., Cambridge, MA (1976)] and \textit{L. T. Fernholz} [Von Mises calculus for statistical functionals. (1983; Zbl 0525.62031)]. We generalize their methods to multivariate observations. We show that a statistical functional is asymptotically normal if it induces a Hadamard differentiable functional defined on the space \(D[0,1]^p\). This work involves \(p\)-dimensional empirical processes. As an example we illustrate the use of the von Mises method [\textit{R. von Mises}, Ann. Math. Stat. 18, 309-348 (1947; Zbl 0037.08401)] in proving the asymptotic normality of Spearman's rank correlation coefficient.
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62G30
zbMATH DE Number: 844598
zbMATH Keywords: statistical functional
zbMATH Keywords: Hadamard differentiable functional
zbMATH Keywords: empirical processes
zbMATH Keywords: von Mises method
zbMATH Keywords: asymptotic normality
zbMATH Keywords: Spearman's rank correlation coefficient
MaRDI profile type: Publication
full work available at URL: jmva.1995.1064
OpenAlex ID: W2012667234
DOI: 10.1006/JMVA.1995.1064
description: scientific article; zbMATH DE number 844598