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
Recommended Citation
Brown, L. D., DasGupta, A., Marden, J. I., & Politis, D. (2004). Characterizations, Sub and Resampling, and Goodness of Fit. Institute of Mathematical Statistics Lecture Notes - Monograph Series, 45 180-206. http://dx.doi.org/10.1214/lnms/1196285390
Included in
Mathematics Commons, Other Physical Sciences and Mathematics Commons, Statistics and Probability Commons
Date Posted: 27 November 2017