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

Tejas Desai

ISBN 10: 1461464420 / ISBN 13: 9781461464426

Published by Springer New York, Springer New York Feb 2013, 2013

About this Item

Neuware -¿¿¿ 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.¿Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 64 pp. Englisch.

Seller Inventory # 9781461464426

Bibliographic Details

• Title: A Multiple-Testing Approach to the Multivariate Behrens-Fisher Problem
• Publisher: Springer New York, Springer New York Feb 2013
• Publication Date: 2013
• Language: English
• ISBN 10: 1461464420
• ISBN 13: 9781461464426
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 4D millimeters 235 millimeters width by 155 millimeters height by 4 millimeters depth
• Weight: 113 grams

About this title

Synopsis

​​ ​    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. ​

About the Author

Tejas A. Desai is Assistant Professor at The Adani Institute of Infrastructure Management