Agreement probabilities for some CPIT—neyman smooth tests

Abstract

The CPIT transformations do not, in general, give the same set of transformed values for different orderings of the observations in a sample. When these transformations are followed by a test of uniformity to give an overall goodness-of-fit test, it is possible to obtain different results for different orderings of a sample. We consider here the probability that two goodness-of-fit tests based on randomly selected permutations of the same sample and a Neyman smooth uniformity test will .~agree in their conclusions. We observe for the cases considered in a simulation study that the probability of agreement is generally large and tends to one with increasing n. KEY WORDS: Conditional probability integral transformations, Neyman smooth test, agreement probabilities, conjectured lower bound.

Some Transformation Methods in Goodness-of-Fit*

“…A quantity of relevance here is the probability that two tests will agree in their conclusions. Quesenberry and Dietz (1983) considered this probability for Neyman smooth tests made on the U's from random permutations of a sample. They gave empirical evidence that these agreement probabilities are very high in many cases of interest and are bounded below by the value 2/3 for all cases considered.…”