# Download A Multiple-Testing Approach to the Multivariate by Tejas Desai PDF

By Tejas Desai

​​ ​ In statistics, the Behrens–Fisher challenge is the matter of period estimation and speculation trying out about the distinction among the technique of usually dispensed populations whilst the variances of the 2 populations should not assumed to be equivalent, in response to self reliant samples. In his 1935 paper, Fisher defined an method of the Behrens-Fisher challenge. in view that high-speed desktops weren't on hand in Fisher’s time, this procedure was once now not implementable and was once quickly forgotten. thankfully, now that high-speed pcs can be found, this procedure can simply be carried out utilizing only a computing device or a computer desktop. moreover, Fisher’s process used to be proposed for univariate samples. yet this method is also generalized to the multivariate case. during this monograph, we current the answer to the afore-mentioned multivariate generalization of the Behrens-Fisher challenge. we begin out via featuring a try out of multivariate normality, continue to test(s) of equality of covariance matrices, and finish with our option to the multivariate Behrens-Fisher challenge. All equipment proposed during this monograph should be comprise either the randomly-incomplete-data case in addition to the complete-data case. in addition, all equipment thought of during this monograph could be confirmed utilizing either simulations and examples. ​

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Extra info for A Multiple-Testing Approach to the Multivariate Behrens-Fisher Problem: with Simulations and Examples in SAS®

Sample text

To consider the first alternative, we generate data with the same covariance matrices as in Sect. 1, but the mean vectors being f0 0 0 0 0g, f0 0 0 0 0g, and f0 0 1 1 1g. 12 demonstrates that method B can be a strong contender to method A in terms of power for the type of alternative considered. Let us now consider another alternative with mean vectors being f0 0 1 0 0g, f0 0 0 1 0g, and f0 0 0 0 1g. 13 is left as an exercise to the reader. 3 Example: Wisconsin Nursing Home Study Revisited In Sect.

As a further motivation, the k-sample ANOVA problem is presented where k > 2. Finally, we present the heteroscedastic MANOVA problem to which all the three approaches are applied. For the k-sample ANOVA problem, k > 2, and for the heteroscedastic MANOVA problem, we use the FDR algorithm. Type I errors and power for each method are also presented. Finally, two examples are also presented. Keywords ANOVA • Behrens–Fisher problem • False discovery rate • Heteroscedasticity • MANOVA • Power • Type I errors Suppose a data analyst wants to test for equality of multivariate mean vectors when there is statistical evidence to believe that the underlying covariance matrices are not equal, but that there is evidence that the distributions generating the data are multivariate normal.

As a motivation, we begin with the two-sample ANOVA problem to which all the three approaches are applied. As a further motivation, the k-sample ANOVA problem is presented where k > 2. Finally, we present the heteroscedastic MANOVA problem to which all the three approaches are applied. For the k-sample ANOVA problem, k > 2, and for the heteroscedastic MANOVA problem, we use the FDR algorithm. Type I errors and power for each method are also presented. Finally, two examples are also presented. Keywords ANOVA • Behrens–Fisher problem • False discovery rate • Heteroscedasticity • MANOVA • Power • Type I errors Suppose a data analyst wants to test for equality of multivariate mean vectors when there is statistical evidence to believe that the underlying covariance matrices are not equal, but that there is evidence that the distributions generating the data are multivariate normal.