Balakrishnan N., Rao C.R. Order statistics. Theory and Methods

Elsevier, 1998. — 752 p.The area of Order Statistics received a tremendous attention from numerous researchers during the past century. During this period, several major theoretical advances were made in this area of research. As a matter of fact, two of those have been adjudged as breakthroughs in the field of Statistics [see: Kotz, S. and Johnson, N. L. (1991). Breakthroughs in Statistics, Vols. 1 and 2, Springer-Verlag, New York]. In the course of these developments, order statistics have also found important applications in many diverse areas including life-testing and reliability, robustness studies, statistical quality control, filtering theory, signal processing, image processing, and radar target detection.
Based on this immense activity, we decided to prepare this Handbook on Order Statistics and Their Applications. We feel that we have successfully brought together theoretical researchers working on theoretical and methodological advancements on order statistics and applied statisticians and engineers developing new and innovative applications of order statistics. Altogether, there are 44 articles covering most of the important theoretical and applied aspects of order statistics. For the convenience of readers, the subject matter has been divided into two volumes, the first one (Handbook-16, /file/1799261/, /file/1799262) focusing on Theory and Methods and the second one (Handbook-17, /file/1799276/, /file/1799277) dealing primarily with Applications. Each volume has also been organized according to different parts, with each part specializing on one aspect of Order Statistics.Part I. Introduction and Basic Properties
Order Statistics: An Introduction
Order Statistics: A Historical Perspective
Computer Simulation of Order Statistics
Part II. Orderings and Bounds
Lorenz Ordering of Order Statistics and Record Values
Stochastic Ordering of Order Statistics
Bounds for Expectations of L-Estimates
Part III. Relations and Identities
Recurrence Relations and Identities for Moments of Order Statistics
Part IV. Characterizations
Recent Approaches to Characterizations Based on Order Statistics and Record Values
Characterizations of Distributions via Identically Distributed Functions of Order Statistics
Characterizations of Distributions by Recurrence Relations and Identities for Moments of Order Statistics
Part V. Extremes and Asymptotics
Univariate Extreme Value Theory and Applications
Order Statistics: Asymptotics in Applications
Zero-One Laws for Large Order Statistics
Part VI. Robust Methods
Some Exact Properties Of Cook's DJ
Generalized Recurrence Relations for Moments of Order Statistics from Non-Identical Pareto and Truncated Pareto Random Variables with Applications to Robustness
Part VII. Resampling Methods
A Semiparametric Bootstrap for Simulating Extreme Order Statistics
Approximations to Distributions of Sample Quantiles
Part VIII. Related Statistics
Concomitants of Order Statistics
A Record of Records
Part IX. Related Processes
Weighted Sequential Empirical Type Processes with Applications to Change-Point Problems
Sequential Quantile and Bahadur-Kiefer Processes