A1315
Title: Moment-generating function of the Hettmansperger-Norton-type test for patterned alternatives
Authors: Hikaru Yamaguchi - Tokyo University of Science (Japan) [presenting]
Hidetoshi Murakami - Tokyo University of Science (Japan)
Abstract: Testing the equality of several location parameters against patterned alternatives, such as ordered or umbrella alternatives, is one of the intriguing subjects in nonparametric statistics. For example, in dose-response studies, the drug effect on animals is expected to increase or decrease as the dosage increases. In such cases, an ordered alternative model is suitable. The Hettmansperger-Norton-type test, defined as a linear combination of linear rank statistics, is a frequently used nonparametric rank test for patterned alternatives. The moment-generating function of the Hettmansperger-Norton-type test is derived in the presence of ties. Furthermore, the explicit formulas of some higher-order moments are also derived to obtain the Edgeworth approximation for the null distribution of the test statistic. Simulation studies demonstrate the usefulness of the Edgeworth approximation by examining the Type I error rate in the case of small sample sizes.
