The Annals of Statistics
- Ann. Statist.
- Volume 1, Number 1 (1973), 74-83.
The Conditional Probability Integral Transformation and Applications to Obtain Composite Chi-Square Goodness-of-Fit Tests
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.
Ann. Statist., Volume 1, Number 1 (1973), 74-83.
First available in Project Euclid: 25 October 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
O'Reilly, Federico J.; Quesenberry, C. P. The Conditional Probability Integral Transformation and Applications to Obtain Composite Chi-Square Goodness-of-Fit Tests. Ann. Statist. 1 (1973), no. 1, 74--83. doi:10.1214/aos/1193342383. https://projecteuclid.org/euclid.aos/1193342383