Order Statistics (Wiley Series on Human Communication) - Hardcover

H. A. David

Hardcover

ISBN 10: 0471196754 ISBN 13: 9780471196754

Publisher: John Wiley & Sons Inc, 1970

Synopsis

Other volumes in the Wiley Series in Probability and Mathematical Statistics The Theory of Linear Models and Multivariate Analysis Steven F. Arnold Presents a detailed, theoretical treatment of models that assume an underlying normal distribution. Considers the univariate linear, generalized linear, repeated measures, random effects, mixed, correlation, multivariate linear and discrimination models. Optimal estimation and testing procedures and simultaneous confidence intervals are derived for each. Emphasizes the similarity of univariate and multivariate models. Uses a co-ordinate free notation in which most of the important statistics are defined as projections on particular subspaces or the lengths of such projections. 1981 Approximation Theorems of Mathematical Statistics Robert J. Serfling This book covers asymptotic distribution theory, consistency properties, and asymptotic relative efficiency approaches. It includes methods of proof and emphasizes the manipulation of probability theorems for statistical use. Besides standard types of statistics such as the empirical distribution function, the sample moments, sample quantiles, maximum likelihood estimates, etc., Serfling treats special classes of statistics: U-statistics, differentiable statistical functions, Mestimates, L-estimates, and R-estimates. A readily accessible text for students in statistics, general mathematics, operations research, and selected engineering fields. 1980 Robust Statistics Peter J. Huber A systematic, book-length treatment of the subject. Begins with a general introduction and the formal mathematical background behind qualitative and quantitative robustness. Stresses concepts. Provides selected numerical algorithms for computing robust estimates, as well as convergence proofs. Tables contain quantitative robustness information for a variety of estimates. 1980

About this title

From the Back Cover

A completely revised and expanded edition of a classic resource

In the over twenty years since the publication of the Second Edition of Order Statistics, the theories and applications of this dynamic field have changed markedly. Meeting the challenges and demands of today’s students and research community, authors H. A. David and H. N. Nagaraja return with a completely revised and updated Order Statistics, Third Edition.

Chapters two through nine of this comprehensive volume deal with finite-sample theory, with individual topics grouped under distribution theory (chapters two through six) and statistical inference (chapters seven through nine). Chapters ten and eleven cover asymptotic theory for central, intermediate, and extreme order statistics, representing twice the coverage of this subject than the previous edition. New sections include:

• Stochastic orderings
• Characterizations
• Distribution-free prediction intervals
• Bootstrap estimations
• Moving order statistics
• Studentized range
• Ranked-set sampling
• Estimators of tail index

The authors further explain application procedures for many data-analysis techniques and quality control. An appendix provides a guide to related tables and computer algorithms. Extensive exercise sets have been updated since the last edition. In spite of many eliminations, the total number of references has increased from 1,000 to 1,500.

Expanded coverage of shortcut methods, robust estimation, life testing, reliability, L-statistics, and extreme-value theory complete this one-of-a-kind resource. Students and researchers of order statistics will appreciate this updated and thorough edition.

From the Inside Flap

This volume is a unified, thoroughly updated treatment of both the theory and applications of ordered random variables and functions thereof. Familiar examples of such order statistics are the extremes, the range, the extreme-deviate, and the studentized range. The text provides systematic development of the distribution theory of order statistics for discrete as well as continuous populations. Important applications covered include procedures for the treatment of outliers and other techniques commonly placed under the heading of data analysis. Short-cut methods, robust estimation, lifetesting, reliability, and extreme-value theory are all dealt with. Also, this latest edition features new material on order statistics for independent nonidentically distributed variates, linear functions of order statistics (in finite samples), concomitants of order statistics, and testing for outliers from a regression model. The section on robust estimation has been greatly expanded and much of the material on asymptotic theory of order statistics has been completely rewritten. Many exercises, most with an indication of source in the literature, an extensive, expanded set of references on all aspects of the subject, and a guide to the numerous tables that are essential for the ready use of the methodology, complement the text. Order Statistics, 2nd Edition continues to provide up-to-date, comprehensive treatment of this growing field. Statisticians, graduate students and users of statistics throughout academia, industry and government will find this a most valuable guide to the theory, methodology, applications, and original literature of order statistics.

Edition details

• Publisher: John Wiley & Sons Inc
• Publication date: 1970
• Language: English
• ISBN 10: 0471196754
• ISBN 13: 9780471196754
• Binding: Hardcover
• Edition number: 1
• Number of pages: 288