Accession Number : AD0755295

Title :   Optimal Invariant Tests for Uniformity.

Descriptive Note : Technical rept.,

Corporate Author : PRINCETON UNIV N J DEPT OF STATISTICS

Personal Author(s) : Watson,G. S.

Report Date : NOV 1972

Pagination or Media Count : 16

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)

Descriptors :   (*STATISTICAL TESTS, INVARIANCE), PROBABILITY DENSITY FUNCTIONS, TOPOLOGY, APPROXIMATION(MATHEMATICS)

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE