Data driven versions of neyman's test for uniformity based on bayesian rule

Abstract

The paper is concerned with a modification of the data driven version of Neyman's testfor uniformity proposed by Ledwina (1994). The number of components in Ledwina'stest is chosen by Schwan rule. It is known that for small sample sizes the rule has a tendency to underestimate the model dimension. This gave a mdtivation for the present paper in which we examine an alternative criterion for the choice of the number of cornponents in the smooth test statistic. Schwan rule is an approximation of a Bayesian rule for the choice of the dimension of the exponential model. Trying to improve properties of Ledwina's test we turn to the more aocurate approximation of the Bayesian rule derived by Haughton (1988). Siulations ahow that by the appropriate choice of the prior distribution one obtains a rule which is more flexible than Schwan rule and the resulting test performs even better than the original Ledwina's test. We also give some asymptotic results on the null distribution and consistency of the introduced test.

Keywords:

• Schwan BIC criterion
• Exponential family
• Goodness-of-fit test
• Smooth test
• Neyman's test
• Monte Carlo simulations