An invariance principle for U-statistics in simple random sampling without replacement
type: Item
instance of: scholarly article
title: An invariance principle for U-statistics in simple random sampling without replacement
zbMATH Open document ID: 0652.62010
DOI: 10.1007/BF02613149
published in: Metrika
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/176119
review text: Supplementing the well-known invariance principle for U-statistics based on i.i.d. observations [\textit{R. G. Miller} and \textit{P. K. Sen}, Ann. Math. Stat. 43, 31-41 (1972; Zbl 0238.62057)] we establish an invariance pinciple for U-statistics in case of simple random sampling from a sequence of finite populations. This generalizes the asymptotic normality result of \textit{H. K. Nandi} and \textit{P. K. Sen} [Calcutta Stat. Assoc. Bull. 12, 124-148 (1963; Zbl 0123.370)], and permits e.g. to prove asymptotic normality of U-statistics in the presence of random non- response.
Mathematics Subject Classification ID: 62D05
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 4064240
zbMATH Keywords: simple random sampling without replacement
zbMATH Keywords: invariance pinciple for U- statistics
zbMATH Keywords: finite populations
zbMATH Keywords: asymptotic normality
zbMATH Keywords: random non-response
author: Hartmut Milbrodt
MaRDI profile type: Publication
cites work: Q5560061
cites work: Q3756303
cites work: Weak Convergence of $U$-Statistics and Von Mises' Differentiable Statistical Functions
cites work: On the Properties of U-Statistics When the Observations are not Independent
cites work: Q5619558
description: scientific article; zbMATH DE number 4064240