Goodness of fit tests using regression

Abstract

A method for developing distribution-free goodness-of-fit tests for a completely specified continuous distribution is pre- sented. A transformation of the n order statistics of a random sample into a set of n statistics is given. Under the null hypothesis these statistics are identically and independently distributed as standard normal random variables. If an alter- native distribution is true, the transformed values tend to exhi- bit systematic behavior. The absence of such behavior may be tested by a regression of the transformed values on their orders. Several representative test procedures are presented and each is shown to have either a chi-squared or variance ratio distribu- tion when the null hypothesis is true thereby obviating the need for special tables. The simple null distributions of the pro- posed test statistics set these procedures apart from competing tests. Exact, weak Bahadur efficiences for some of the tests are developed. Monte Carlo results are given which compare the power of the pr...