GOODNESS-OF-FIT TESTS BASED ON CHARACTERIZATION OF UNIFORMITY BY THE RATIO OF ORDER STATISTICS, AND THEIR EFFICIENCY

摘要

We construct integral and supremum type goodness-of-fit tests for the uniform law based on Ah-sanullah's characterization of the uniform law. We discuss limiting distributions of new tests and describe the logarithmic large deviation asymptotics of test statistics under null-hypothesis. This enables us to calculate their local Bahadur efficiency under some parametric alternatives. Conditions of local optimality of new statistics are given.