Optimal Invariant Tests for Uniformity.
PRINCETON UNIV N J DEPT OF STATISTICS
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The Kolmogorov and Cramer-von Mises families of tests for uniformity on the unit interval are not derived as optimal tests. However on the circle and its generalizations, it is possible to derive optimal invariant tests for uniformity. Beran 1968 studied tests of local alternatives. These have the integral square form. Watsons 1961 circular variant of the Cramer-von Mises test was shown to be optimal in a certain situation. In the paper, tests for distant alternatives are derived. These have the supremum form. Circular variants of D sub n and D sub n- are shown to be optimal. Author
- Statistics and Probability