Statistics Papers

Document Type

Journal Article

Date of this Version

2004

Publication Source

Institute of Mathematical Statistics Lecture Notes - Monograph Series

Volume

45

Start Page

180

Last Page

206

DOI

10.1214/lnms/1196285390

Abstract

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.

Keywords

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

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Date Posted: 27 November 2017