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A Multiple-Testing Approach to the Multivariate Behrens-Fisher Problem [electronic resource] : with Simulations and Examples in SAS® / by Tejas Desai.

By: Desai, Tejas [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: SpringerBriefs in Statistics: Publisher: New York, NY : Springer New York : Imprint: Springer, 2013Description: V, 55 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9781461464433.Subject(s): Statistics | Mathematical statistics | Statistics | Statistical Theory and Methods | Statistics, general | Statistics and Computing/Statistics ProgramsDDC classification: 519.5 Online resources: Click here to access online
Contents:
Introduction -- On Testing for Multivariate Normality -- On Testing Equality of Covariance Matrices -- On Heteroscedastic MANOVA -- References.
In: Springer eBooksSummary:    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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Introduction -- On Testing for Multivariate Normality -- On Testing Equality of Covariance Matrices -- On Heteroscedastic MANOVA -- References.

   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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