A simulation study of the robustness of Hotelling’s T2 test for the mean of a multivariate distribution when sampling from a multivariate skew-normal distribution

dc.contributor.authorWu, Yun
dc.date.accessioned2009-10-29T14:57:47Z
dc.date.available2009-10-29T14:57:47Z
dc.date.graduationmonthDecemberen_US
dc.date.issued2009-10-29T14:57:47Z
dc.date.published2009en_US
dc.description.abstractHotelling’s T2 test is the standard tool for inference about the mean of a multivariate normal population. However, this test may perform poorly when used on samples from multivariate distributions with highly skewed marginal distributions. The goal of our study was to investigate the type I error rate and power properties of Hotelling’s one sample test when sampling from a class of multivariate skew-normal (SN) distributions, which includes the multivariate normal distribution and, in addition to location and scale parameters, has a shape parameter to regulate skewness. Simulation results of tests carried out at nominal type I error rate 0.05 obtained from various levels of shape parameters, sample sizes, number of variables and fixed correlation matrix showed that Hotelling’s one sample test provides adequate control of type I error rates over the entire range of conditions studied. The test also produces suitable power levels for detecting departures from hypothesized values of a multivariate mean vector when data result from a random sample from a multivariate SN. The shape parameter of the SN family appears not to have much of an effect on the robustness of Hotelling’s test. However, surprisingly, it does have a positive impact on power.en_US
dc.description.advisorPaul I. Nelsonen_US
dc.description.degreeMaster of Scienceen_US
dc.description.departmentDepartment of Statisticsen_US
dc.description.levelMastersen_US
dc.identifier.urihttp://hdl.handle.net/2097/1939
dc.language.isoen_USen_US
dc.publisherKansas State Universityen
dc.subjectSimulation studyen_US
dc.subjectHotelling's T2 testen_US
dc.subjectSkew normalen_US
dc.subject.umiStatistics (0463)en_US
dc.titleA simulation study of the robustness of Hotelling’s T2 test for the mean of a multivariate distribution when sampling from a multivariate skew-normal distributionen_US
dc.typeReporten_US

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