Simon Fraser University - Department of Statistics and Actuarial Science
I discuss the impact of three principles on the problem of choosing a good goodness-of-fit test. First: when testing statistical hypotheses alternatives of interest are neither indetectably nor grossly different from the null hypothesis. Second, good tests are designed to be sensitive to alternatives likely to arise in practice. Third, the purpose of limit theorems is to provide good approximate probability calculations of interest to statisticians.
I will use Bayesian priors on the alternative hypothesis to construct tests which maximize the expected power for a prior which depends on the sample size. Priors will be presented for which the optimal procedures are (approximately) such goodness-of-fit tests as the CramÃ©r-von Mises or the Anderson-Darling test.