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Statistics - Statistical Theory and Methods | A Multiple-Testing Approach to the Multivariate Behrens-Fisher Problem

A Multiple-Testing Approach to the Multivariate Behrens-Fisher Problem

with Simulations and Examples in SAS®

Desai, Tejas

2013, V, 55 p.

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  • ​​Applies aspects of multivariate normality to the concept of hypothesis testing
  • Introduces a novel multivariate solution to a long-standing statistical problem ​
​​ ​    In statistics, the Behrens–Fisher problem is the problem of interval estimation and hypothesis testing concerning the difference between the means of two normally distributed populations when the variances of the two populations are not assumed to be equal, based on two independent samples. In his 1935 paper, Fisher outlined an  approach to the Behrens-Fisher problem.  Since high-speed computers were not available in Fisher’s time, this approach was not implementable and was soon forgotten. Fortunately, now that high-speed computers are available, this approach can easily be implemented using just a desktop or a laptop computer. Furthermore, Fisher’s approach was proposed for univariate samples. But this approach can also be generalized to the multivariate case.      In this monograph, we present the solution to the afore-mentioned multivariate generalization of the Behrens-Fisher problem.  We start out by presenting  a test of multivariate normality, proceed to test(s) of equality of covariance matrices, and end with our solution to the multivariate Behrens-Fisher problem. All methods proposed in this monograph will be include both the randomly-incomplete-data case as well as the complete-data case. Moreover, all methods considered in this monograph will be tested using both simulations and examples. ​

Content Level » Research

Keywords » Fisher-Behrens Problem - SAS - covariance matrices - multiple-testing - multivariate analysis - simulation

Related subjects » Computational Statistics - Statistical Theory and Methods - Statistics

Table of contents 

Introduction.- On Testing for Multivariate Normality.- On Testing Equality of Covariance Matrices.- On Heteroscedastic MANOVA.- References.

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