Optimal Invariant Tests for Uniformity.
Abstract
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. Watson's (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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1972
- Accession Number
- AD0755295
Entities
People
- G. S. Watson
Organizations
- Princeton University