EAN: 9781461464426

SPRINGERBRIEFS IN STATISTICS A MULTIPLE-TESTI...

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.

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