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April 2000 Resampling and exchangeable arrays
Peter Mccullagh
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Bernoulli 6(2): 285-301 (April 2000).


The nonparametric, or resampling, bootstrap for a single unstructured sample corresponds to the algebraic operation of monoid composition, with a uniform distribution on the monoid. With this interpretation, the notion of resampling can be extended to designs having a certain group-invariance property. Two types of exchangeable array structures are considered in some detail, namely the one-way layout, and the two-way row-column exchangeable design. Although in both cases there is a unique group under which the sampling distribution of the observations is exchangeable, the choice of monoid is not unique. Different choices of monoid can lead to drastically different, and in some cases quite misleading, inferences.


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Peter Mccullagh. "Resampling and exchangeable arrays." Bernoulli 6 (2) 285 - 301, April 2000.


Published: April 2000
First available in Project Euclid: 12 April 2004

zbMATH: 0976.62035
MathSciNet: MR2001F:62030

Keywords: bootstrap , exchangeability , group invariance , monoid composition , product monoid , symmetric function

Rights: Copyright © 2000 Bernoulli Society for Mathematical Statistics and Probability


Vol.6 • No. 2 • April 2000
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