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Field name	Details
Dewey Class	519
Title	Approximate Distributions of Order Statistics ([EBook]) : With Applications to Nonparametric Statistics / by R.-D. Reiss.
Author	Reiss, Rolf-Dieter
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : Springer , 1989.
Physical Details	XII, 355 pages : online resource.
Series	Springer Series in Statistics 0172-7397
ISBN	9781461396208
Summary Note	This book is designed as a unified and mathematically rigorous treatment of some recent developments of the asymptotic distribution theory of order statistics (including the extreme order statistics) that are relevant for statistical theory and its applications. Particular emphasis is placed on results concern ing the accuracy oflimit theorems, on higher order approximations, and other approximations in quite a general sense. Contrary to the classical limit theorems that primarily concern the weak convergence of distribution functions, our main results will be formulated in terms of the variational and the Hellinger distance. These results will form the proper springboard for the investigation of parametric approximations of nonparametric models of joint distributions of order statistics. The approxi mating models include normal as well as extreme value models. Several applications will show the usefulness of this approach. Other recent developments in statistics like nonparametric curve estima tion and the bootstrap method will be studied as far as order statistics are concerned. 1n connection with this, graphical methods will, to some extent, be explored.:
Contents note	0 Introduction -- 0.1. Weak and Strong Convergence -- 0.2. Approximations -- 0.3. The Role of Order Statistics in Nonparametric Statistics -- 0.4. Central and Extreme Order Statistics -- 0.5. The Restriction to Independent and Identically Distributed Random Variables -- 0.6. Graphical Methods -- 0.7. A Guide to the Contents -- 0.8. Notation and Conventions -- I Exact Distributions and Basic Tools -- 1 Distribution Functions, Densities, and Representations -- 2 Multivariate Order Statistics -- 3 Inequalities and the Concept of Expansions -- II Asymptotic Theory -- 4 Approximations to Distributions of Central Order Statistics -- 5 Approximations to Distributions of Extremes -- 6 Other Important Approximations -- 7 Approximations in the Multivariate Case -- III Statistical Models and Procedures -- 8 Evaluating the Quantile and Density Quantile Function -- 9 Extreme Value Models -- 10 Approximate Sufficiency of Sparse Order Statistics -- Appendix 1. The Generalized Inverse -- Appendix 2. Two Technical Lemmas on Expansions -- Appendix 3. Further Results on Distances of Measures -- Author Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4613-9620-8
Links to Related Works	Subject References: Applications of Mathematics . Applied mathematics . Engineering mathematics . Mathematics . Authors: Reiss, Rolf-Dieter . Reiss, Rolf-Dieter . Corporate Authors: SpringerLink (Online service) . Series: Springer Series in Statistics . Classification: 519 .

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Approximate Distributions of Order Statistics: With Applications to Nonparametric Statistics

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