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, under alternative hypotheses.

Keywords:

• Conditional probability integral transformations
• Neyman smooth test
• agreement probabilities
• conjectured lower bound