Order Statistics: Theory and Methods

About this book

Major theoretical advances were made in this area of research, and in the course of these developments order statistics has also found important applications in many diverse areas. These include life-testing and reliability, robustness studies, statistical quality control, filtering theory, signal processing, image processing, and radar target detection.

Theoretical researchers working on theoretical and methodological advancements on order statistics and applied statisticians and engineers developing new and innovative applications of order statistics have been successfully brought together to create this handbook. For the convenience of readers, the subject matter has been divided into two volumes. This volume focuses on theory and methods, and volume 17 deals primarily with applications. Each volume has been divided into parts, each part specializing in one aspect of order statistics. The articles in this volume have been classified into nine parts. An elaborate Author Index as well as a Subject Index is presented in both volumes in order to facilitate easy access to all the material included in this volume.

These two volumes form a useful and valuable reference work for theoretical researchers, applied scientists and engineers, and graduate students involved in the area of order statistics.

Contents

Part 1 Introduction and basic properties; order statistics - an introduction; order statistics - an historical perspective; computer simulation of order statistics. Part 2 Orderings and bounds: Lorenz ordering of order statistics and record values; bounds for expectations of L-estimates. Part 3 Relations and identities: recurrence, relations and identities for moments of order statistics. Part 4 Characterization: recent approaches to characterizations based on order statistics and record values; characterization of distributions via identically distributed functions of order statistics; characterizations of distributions by recurrence relations and identities for moments of order statistics. Part 5 Extremes and asymptotics: univariate extreme value theory and applications; order statistics - asymptotics in applications; zero-one laws for large order statistics. Part 6 Robust methods: some exact properties of Cook's D1; generalized recurrence relations for moments of order statistics from non-identical Pareto and truncated Pareto random variables with applications to robustness. Part 7 Resampling methods: a semiparametric bootstrap for simulating extreme order statistics; approximations to distributions of sample quantiles. Part 8 Related statistics: concomitants of order statistics; a record of records. Part 9 Related processes: weighted sequential empirical type processes with applications to change-point problems; sequential quantile and Bahadur-Kiefer processes.

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