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VOL. 45 | 2004 Characterizations, Sub and resampling, and goodness of fit
L. Brown, Anirban DasGupta, John Marden, Dimitris Politis

Editor(s) Anirban DasGupta


We present a general proposal for testing for goodness of fit, based on resampling and subsampling methods, and illustrate it with graphical and analytical tests for the problems of testing for univariate or multivariate normality. The proposal shows promising, and in some cases dramatic, success in detecting nonnormality. Compared to common competitors, such as a Q-Q plot or a likelihood ratio test against a specified alternative, our proposal seems to be the most useful when the sample size is small, such as 10 or 12, or even very small, such as 6! We also show how our proposal provides tangible information about the nature of the true cdf from which one is sampling. Thus, our proposal also has data analytic value. Although only the normality problem is addressed here, the scope of application of the general proposal should be much broader.


Published: 1 January 2004
First available in Project Euclid: 28 November 2007

zbMATH: 1268.62042
MathSciNet: MR2126897

Digital Object Identifier: 10.1214/lnms/1196285390

Primary: 62E10 , 62G09

Keywords: bootstrap , characterization , consistency , goodness of fit , multivariate normal , normal , power , Q-Q plot , scatterplot , subsampling

Rights: Copyright © 2004, Institute of Mathematical Statistics


Vol. 45 • 1 January 2004
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