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 BehrensFisher Problem and Its Extension

Author(s):

Jiajuan Liang* and Guoliang Tian and ManLai Tang and Jing Yang

Companies:

BNUHKBU United International College and Southern University of Science and Technology and The Hang Seng University of Hong Kong and Tianjin Medical University

Keywords:

BehrensFisher problem;
Ftest;
Multiple mean comparison;
Spherical distributions

Abstract:

It is wellknown that the classical BehrensFisher problem originated from comparing two univariate normal means. The problem can be extended to comparing multiple normal means without the equalvariance assumption. This violates the usual equalvariance 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 BehrensFisher problem has not yet been satisfactorily obtained. In this paper, we develop a new approach to obtaining an exact solution to the BehrensFisher problem and its extension using the theory of spherical distributions. A class of simple statistics with the usual Fdistribution 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.
