Combinatorial stochastic processes
type: Item
instance of: scholarly article
title: Combinatorial stochastic processes
zbMATH Open document ID: 0808.60027
DOI: 10.1016/0304-4149(94)90101-5
author: Lutz Dümbgen
published in: Stochastic Processes and their Applications
publication date: 1995-03-12T00:00:00Z
full work available at URL: beitrag.12.pdf
review text: Well-known asymptotic results for sums of independent stochastic processes are extended to processes \(S = \sum^ n_{i = 1} \varphi_{i \pi (i)}\), where \(\varphi = (\varphi_{ij})_{1 \leq i,j \leq n}\) is a collection of independent stochastic processes \(\varphi_{ij}\) on some set \(\tau\), and \(\pi\) is a random permutation of \(\{1,2, \dots, n\}\) such that \(\pi\), \(\varphi\) are independent. The general results, a uniform law of large numbers and a functional central limit theorem, are applied to permutation processes and randomized trials. Classical applications are rank tests and permutation tests.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 62G10
Mathematics Subject Classification ID: 62G15
zbMATH DE Number: 672061
zbMATH Keywords: symmetrization
zbMATH Keywords: permutation process
zbMATH Keywords: randomized trials
zbMATH Keywords: conservative procedures
zbMATH Keywords: random permutation
zbMATH Keywords: functional central limit theorem
reviewed by: Ludwig Paditz
MaRDI profile type: Publication
OpenAlex ID: W2087739751
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description: scientific article; zbMATH DE number 672061