Author: Mohammad Ahsanullah
Publisher: Nova Publishers
ISBN: 9781594540714
Category : Mathematics
Languages : en
Pages : 252
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Book Description
A lot of probabilists and statisticians, as well as actuarial mathematicians, reliability engineers, meteorologists, hydrologists, economists, business and sport analysts, very often deal with order statistics, which plays an important role in various fields of statistics and its applications. The authors suggest an approach to studying order statistics which proposes an active participation of our reader in the studying process. This book enables a reader to check his/her level of understanding of the theory of order statistics. It gives basic formulae (without proof), which are most important in the theory, and presents a lot of examples, which illustrate the theoretical statements.
Author: Barry C. Arnold
Publisher: SIAM
ISBN: 0898716489
Category : Mathematics
Languages : en
Pages : 291
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Book Description
This updated classic text will aid readers in understanding much of the current literature on order statistics: a flourishing field of study that is essential for any practising statistician and a vital part of the training for students in statistics. Written in a simple style that requires no advanced mathematical or statistical background, the book introduces the general theory of order statistics and their applications. The book covers topics such as distribution theory for order statistics from continuous and discrete populations, moment relations, bounds and approximations, order statistics in statistical inference and characterisation results, and basic asymptotic theory. There is also a short introduction to record values and related statistics. The authors have updated the text with suggestions for further reading that may be used for self-study. Written for advanced undergraduate and graduate students in statistics and mathematics, practising statisticians, engineers, climatologists, economists, and biologists.
Author: Rolf-Dieter Reiss
Publisher: Springer Science & Business Media
ISBN: 1461396204
Category : Mathematics
Languages : en
Pages : 363
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Book Description
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.
Author:
Publisher:
ISBN:
Category : Weights and measures
Languages : en
Pages : 574
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Book Description
Author: Pranab K. Sen
Publisher: Cambridge University Press
ISBN: 0521877229
Category : Mathematics
Languages : en
Pages : 399
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Book Description
A broad view of exact statistical inference and the development of asymptotic statistical inference.
Author: Mohammad Ahsanullah
Publisher: Springer Science & Business Media
ISBN: 949121683X
Category : Mathematics
Languages : en
Pages : 241
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Book Description
This book presents the theory of order statistics in a way, such that beginners can get easily acquainted with the very basis of the theory without having to work through heavily involved techniques. At the same time more experienced readers can check their level of understanding and polish their knowledge with certain details. This is achieved by, on the one hand, stating the basic formulae and providing many useful examples to illustrate the theoretical statements, while on the other hand an upgraded list of references will make it easier to gain insight into more specialized results. Thus this book is suitable for a readership working in statistics, actuarial mathematics, reliability engineering, meteorology, hydrology, business economics, sports analysis and many more.
Author: Harman Leon Harter
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 196
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Book Description
Author: Manfred Denker
Publisher: Birkhäuser
ISBN: 3034892543
Category : Science
Languages : en
Pages : 121
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Book Description
These notes are based on lectures presented during the seminar on " Asymptotic Statistics" held at SchloB Reisensburg, Gunzburg, May 29-June 5, 1988. They consist of two parts, the theory of asymptotic expansions in statistics and probabilistic aspects of the asymptotic distribution theory in nonparametric statistics. Our intention is to provide a comprehensive presentation of these two subjects, leading from elementary facts to the advanced theory and recent results. Prospects for further research are also included. We would like to thank all participants for their stimulating discussions and their interest in the subjects, which made lecturing very pleasant. Special thanks are due H. Zimmer for her excellent typing. We would also like to take this opportunity to to express our thanks to the Gesellschaft fur mathematische Forschung and to the Deutsche Mathematiker Vereinigung, especially to Professor G. Fischer, for the opportunity to present these lectures and to the Birkhauser Verlag for the publication of these lecture notes. R. Bhattacharya, M. Denker Part I: Asymptotic Expansions in Statistics Rabi Bhattacharya 11 {sect}1. CRAMER-EDGEWORTH EXPANSIONS Let Q be a probability measure on (IRk, B"), B" denoting the Borel sigmafield on IR". Assume that the s - th absolute moment of Q is finite, (1.1) P. := J II x lis Q(dx)
Author: A. W. van der Vaart
Publisher: Cambridge University Press
ISBN: 9780521784504
Category : Mathematics
Languages : en
Pages : 470
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Book Description
This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit experiments, which gives the book one of its unifying themes. This entails mainly the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation. Thus, even the standard subjects of asymptotic statistics are presented in a novel way. Suitable as a graduate or Master s level statistics text, this book will also give researchers an overview of the latest research in asymptotic statistics.
Author: Sergey Bobkov
Publisher: American Mathematical Soc.
ISBN: 1470436507
Category : Education
Languages : en
Pages : 138
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Book Description
This work is devoted to the study of rates of convergence of the empirical measures μn=1n∑nk=1δXk, n≥1, over a sample (Xk)k≥1 of independent identically distributed real-valued random variables towards the common distribution μ in Kantorovich transport distances Wp. The focus is on finite range bounds on the expected Kantorovich distances E(Wp(μn,μ)) or [E(Wpp(μn,μ))]1/p in terms of moments and analytic conditions on the measure μ and its distribution function. The study describes a variety of rates, from the standard one 1n√ to slower rates, and both lower and upper-bounds on E(Wp(μn,μ)) for fixed n in various instances. Order statistics, reduction to uniform samples and analysis of beta distributions, inverse distribution functions, log-concavity are main tools in the investigation. Two detailed appendices collect classical and some new facts on inverse distribution functions and beta distributions and their densities necessary to the investigation.
