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Activity Number: 245 - SLDS CSpeed 4
Type: Contributed
Date/Time: Wednesday, August 11, 2021 : 10:00 AM to 11:50 AM
Sponsor: Section on Statistical Learning and Data Science
Abstract #318218
Title: An Exact Solution to the Univariate Behrens-Fisher Problem and Its Extension
Author(s): Jiajuan Liang* and Guoliang Tian and Man-Lai Tang and Jing Yang
Companies: BNU-HKBU United International College and Southern University of Science and Technology and The Hang Seng University of Hong Kong and Tianjin Medical University
Keywords: Behrens-Fisher problem; F-test; Multiple mean comparison; Spherical distributions

It is well-known that the classical Behrens-Fisher problem originated from comparing two univariate normal means. The problem can be extended to comparing multiple normal means without the equal-variance assumption. This violates the usual equal-variance assumption in classical analysis of variance (ANOVA) for a comparison of multiple normal means. Researchers have been studying this problem for nearly a century. However, a fully exact solution to the Behrens-Fisher problem has not yet been satisfactorily obtained. In this paper, we develop a new approach to obtaining an exact solution to the Behrens-Fisher problem and its extension using the theory of spherical distributions. A class of simple statistics with the usual F-distribution under the null hypothesis is constructed. A Monte Carlo study on the comparison between our approach and some existing ones is carried out. A simple application of our approach is illustrated using real data in medical research.

Authors who are presenting talks have a * after their name.

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