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Notes on the Mack‐Wolfe and Chen‐Wolfe Tests for Umbrella Alternatives
Author(s) -
Chen Y. I.
Publication year - 1991
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710330305
Subject(s) - chen , statistic , mathematics , mathematical economics , class (philosophy) , test statistic , percentile , econometrics , statistics , calculus (dental) , statistical hypothesis testing , computer science , medicine , artificial intelligence , paleontology , biology , dentistry
In this paper we find a class of umbrella alternatives for which the M ACK ‐ WOLFE (1981) peak known test is optimal in the sense of Pitman efficiency. The asymptotic null distribution of the C HEN ‐W OLFE (1989) statistic for the peak‐unknown umbrella alternatives problem is obtained. Some percentiles of the asymptotic distribution computed by simulation are presented.