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February 1999 Exploring interactions in high-dimensional tables: a bootstrap alternative to log-linear models
Bernd Streitberg
Ann. Statist. 27(1): 405-413 (February 1999). DOI: 10.1214/aos/1018031118


Based on a revised Lancaster-type representation of the additive interactions associated with a probability measure, a new approach for the analysis of high-dimensional contingency tables is proposed. The approach is essentially model-free because the additive interaction tensor is merely a convenient reparameterization of the given table. Single interaction terms are investigated using the bootstrap method whose first-order asymptotic validity is immediate. The global structure can be investigated by using the multiple $p$-values given by Holm’s sequentially rejecting multiple testing procedure. The procedure is based on a characterization of the Moebius function as a solution of the simultaneous eigenproblem for all intersection operators in a finite lattice.


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Bernd Streitberg. "Exploring interactions in high-dimensional tables: a bootstrap alternative to log-linear models." Ann. Statist. 27 (1) 405 - 413, February 1999.


Published: February 1999
First available in Project Euclid: 5 April 2002

zbMATH: 0945.62063
MathSciNet: MR1701118
Digital Object Identifier: 10.1214/aos/1018031118

Primary: 62H17
Secondary: 05A18, 06A07, 62E30, 62G09, 62H20, 62J15

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.27 • No. 1 • February 1999
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