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January, 1973 The Conditional Probability Integral Transformation and Applications to Obtain Composite Chi-Square Goodness-of-Fit Tests
Federico J. O'Reilly, C. P. Quesenberry
Ann. Statist. 1(1): 74-83 (January, 1973). DOI: 10.1214/aos/1193342383

Abstract

It is shown that certain conditional distributions, obtained by conditioning on a sufficient statistic, can be used to transform a set of random variables into a smaller set of random variables that are identically and independently distributed with uniform distributions on the interval from zero to one. This result is then used to construct distribution-free tests of fit for composite goodness-of-fit problems. In particular, distribution-free chi-square goodness-of-fit tests are obtained for univariate normal, exponential, and normal linear regression model families of distributions.

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Federico J. O'Reilly. C. P. Quesenberry. "The Conditional Probability Integral Transformation and Applications to Obtain Composite Chi-Square Goodness-of-Fit Tests." Ann. Statist. 1 (1) 74 - 83, January, 1973. https://doi.org/10.1214/aos/1193342383

Information

Published: January, 1973
First available in Project Euclid: 25 October 2007

zbMATH: 0276.62025
MathSciNet: MR362691
Digital Object Identifier: 10.1214/aos/1193342383

Rights: Copyright © 1973 Institute of Mathematical Statistics

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Vol.1 • No. 1 • January, 1973
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