On the Asymptotic Theory of Permutation Statistics

Strasser, Helmut and Weber, Christian (1999) On the Asymptotic Theory of Permutation Statistics. Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science", 27. SFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business, Vienna.


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In this paper limit theorems for the conditional distributions of linear test statistics are proved. The assertions are conditioned by the sigma-field of permutation symmetric sets. Limit theorems are proved both for the conditional distributions under the hypothesis of randomness and under general contiguous alternatives with independent but not identically distributed observations. The proofs are based on results on limit theorems for exchangeable random variables by Strasser and Weber. The limit theorems under contiguous alternatives are consequences of an LAN-result for likelihood ratios of symmetrized product measures. The results of the paper have implications for statistical applications. By example it is shown that minimum variance partitions which are defined by observed data (e.g. by LVQ) lead to asymptotically optimal adaptive tests for the k-sample problem. As another application it is shown that conditional k-sample tests which are based on data-driven partitions lead to simple confidence sets which can be used for the simultaneous analysis of linear contrasts. (author's abstract)

Item Type: Paper
Additional Information: accepted for publication in Mathematical Methods of Statistics, 8, 220-250.
Keywords: conditional inference / permutation tests / limit theorem
Divisions: Departments > Finance, Accounting and Statistics > Statistics and Mathematics
Departments > Informationsverarbeitung u Prozessmanag. > Informationswirtschaft
Departments > Informationsverarbeitung u Prozessmanag. > Produktionsmanagement > Taudes
Departments > Marketing > Service Marketing und Tourismus
Depositing User: Repository Administrator
Date Deposited: 29 Mar 2006 16:46
Last Modified: 22 Oct 2019 00:41
URI: https://epub.wu.ac.at/id/eprint/102


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