On Some Nonparametric Estimates and Tests in the Behrens-Fisher Situation PDF Download

Author: Ponnapalli Venkata Ramachandramurty
Publisher:
ISBN:
Category :
Languages : en
Pages : 166

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Author: Akash Roy
Publisher:
ISBN:
Category : Asymptotic distribution (Probability theory)
Languages : en
Pages :

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Statistical comparison of two independent groups are one of the most frequently occurring inference problems in scientific research. Most of the existing methods available in the literature are not applicable when measurements are taken with dependent replicates, for example when visual acuity or any blood parameters of mice sharing the same cage are measured. In all these scenarios the replicates should neither be assumed to be independent nor be observations coming from different subjects. Furthermore, using a summary measure of the replicates as a single observation would decrease precision of the effect estimates and thus decrease the powers of the test procedures. Thus, there is a need for purely nonparametric flexible methods that can be used for analyzing such data in a unified way. Ranking procedures are known to be a robust and powerful statistical analysis tool for which parametric distributional assumptions are doubtful. So, a solution is proposed for these two sample problems with correlated replicates. The results achieved in our work generalize the ideas on previous attempts for testing the rather strict hypothesis H0 : F1 = F2 or even for testing H0 : p = 1 2 . In comparison to the existing pioneering works, differently weighted estimators of the treatment effect p as well as unbiased variance estimators will be proposed in the current work. Therefore, it is of major interest to estimate the treatment effect and to test whether there is any significant difference between these two groups along with the computation of a confidence interval. Weighted, unweighted as well as optimal versions of the estimators of the treatment effects are investigated and their asymptotic distributions are derived in a closed form. Furthermore, major attention will be given to the accuracy of the tests in terms of controlling the nominal type-I error level as well as their powers when sample sizes are rather small. Here, it will be shown that the distributions of the tests can be approximated using t-distributions with approximated SatterthwaiteWelch degrees of freedom. The degrees of freedom are estimated in such a way that the new methods coincide with the Brunner-Munzel test when single measurements are observed. Extensive simulation studies show favorable performance of the new methods. Application of this method is extensively shown in four different studies involving small sample sizes and different numbers of dependent replicates per unit.

Author:
Publisher:
ISBN:
Category : Weights and measures
Languages : en
Pages : 574

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Author: Tae-Hak Park
Publisher:
ISBN:
Category :
Languages : en
Pages : 518

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Author: Tejas Desai
Publisher: Springer Science & Business Media
ISBN: 1461464439
Category : Mathematics
Languages : en
Pages : 60

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​​ ​ 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. ​

Author: Markus Neuhauser
Publisher: CRC Press
ISBN: 1439867046
Category : Mathematics
Languages : en
Pages : 247

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Nonparametric Statistical Tests: A Computational Approach describes classical nonparametric tests, as well as novel and little-known methods such as the Baumgartner-Weiss-Schindler and the Cucconi tests. The book presents SAS and R programs, allowing readers to carry out the different statistical methods, such as permutation and bootstrap tests. Th

Author: Javier Rojo
Publisher: Springer Science & Business Media
ISBN: 1461414113
Category : Mathematics
Languages : en
Pages : 1103

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These volumes present a selection of Erich L. Lehmann’s monumental contributions to Statistics. These works are multifaceted. His early work included fundamental contributions to hypothesis testing, theory of point estimation, and more generally to decision theory. His work in Nonparametric Statistics was groundbreaking. His fundamental contributions in this area include results that came to assuage the anxiety of statisticians that were skeptical of nonparametric methodologies, and his work on concepts of dependence has created a large literature. The two volumes are divided into chapters of related works. Invited contributors have critiqued the papers in each chapter, and the reprinted group of papers follows each commentary. A complete bibliography that contains links to recorded talks by Erich Lehmann – and which are freely accessible to the public – and a list of Ph.D. students are also included. These volumes belong in every statistician’s personal collection and are a required holding for any institutional library.

Author: Denis Larocque
Publisher:
ISBN:
Category :
Languages : en
Pages : 16

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Author: Myles Hollander
Publisher: Wiley-Interscience
ISBN:
Category : Mathematics
Languages : en
Pages : 900

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An extensive array of examples drawn from actual experiments illustrates clearly how to use nonparametric approaches to handle one- or two-sample location and dispersion problems, dichotomous data, and one-way and two-way layout problems.

Author: Myles Hollander
Publisher: John Wiley & Sons
ISBN: 1118553292
Category : Mathematics
Languages : en
Pages : 872

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Praise for the Second Edition “This book should be an essential part of the personal library of every practicing statistician.”—Technometrics Thoroughly revised and updated, the new edition of Nonparametric Statistical Methods includes additional modern topics and procedures, more practical data sets, and new problems from real-life situations. The book continues to emphasize the importance of nonparametric methods as a significant branch of modern statistics and equips readers with the conceptual and technical skills necessary to select and apply the appropriate procedures for any given situation. Written by leading statisticians, Nonparametric Statistical Methods, Third Edition provides readers with crucial nonparametric techniques in a variety of settings, emphasizing the assumptions underlying the methods. The book provides an extensive array of examples that clearly illustrate how to use nonparametric approaches for handling one- or two-sample location and dispersion problems, dichotomous data, and one-way and two-way layout problems. In addition, the Third Edition features: The use of the freely available R software to aid in computation and simulation, including many new R programs written explicitly for this new edition New chapters that address density estimation, wavelets, smoothing, ranked set sampling, and Bayesian nonparametrics Problems that illustrate examples from agricultural science, astronomy, biology, criminology, education, engineering, environmental science, geology, home economics, medicine, oceanography, physics, psychology, sociology, and space science Nonparametric Statistical Methods, Third Edition is an excellent reference for applied statisticians and practitioners who seek a review of nonparametric methods and their relevant applications. The book is also an ideal textbook for upper-undergraduate and first-year graduate courses in applied nonparametric statistics.