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Order Statistics: Theory and Methods Narayanaswamy Balakrishnan (Distinguished University Professor, Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada)

Order Statistics: Theory and Methods By Narayanaswamy Balakrishnan (Distinguished University Professor, Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada)

Summary

This volume focuses on theory and methods within the area of statistics. Topics covered include: a historical perspective; relations and identities; distributed function of statistics; extremes and asymptotics; and resampling methods.

Order Statistics: Theory and Methods Summary

Order Statistics: Theory and Methods: Volume 16 by Narayanaswamy Balakrishnan (Distinguished University Professor, Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada)

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.

About Narayanaswamy Balakrishnan (Distinguished University Professor, Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada)

Narayanaswamy Balakrishnan is a distinguished university professor in the Department of Mathematics and Statistics at McMaster University Hamilton, Ontario, Canada. He is an internationally recognized expert on statistical distribution theory, and a book-powerhouse with over 24 authored books, four authored handbooks, and 30 edited books under his name. He is currently the Editor-in-Chief of Communications in Statistics published by Taylor & Francis. He was also the Editor-in-Chief for the revised version of Encyclopedia of Statistical Sciences published by John Wiley & Sons. He is a Fellow of the American Statistical Association and a Fellow of the Institute of Mathematical Statistics. In 2016, he was awarded an Honorary Doctorate from The National and Kapodistrian University of Athens, Athens, Greece. In 2021, he was elected as a Fellow of the Royal Society of Canada. Professor C. R. Rao, born in India, is one of this century's foremost statisticians, and received his education in statistics at the Indian Statistical Institute (ISI), Calcutta. He is Emeritus Holder of the Eberly Family Chair in Statistics at Penn State and Director of the Center for Multivariate Analysis. He has long been recognized as one of the world's top statisticians, and has been awarded 34 honorary doctorates from universities in 19 countries spanning 6 continents. His research has influenced not only statistics, but also the physical, social and natural sciences and engineering. In 2011 he was recipient of the Royal Statistical Society's Guy Medal in Gold which is awarded triennially to those "who are judged to have merited a signal mark of distinction by reason of their innovative contributions to the theory or application of statistics". It can be awarded both to fellows (members) of the Society and to non-fellows. Since its inception 120 years ago the Gold Medal has been awarded to 34 distinguished statisticians. The first medal was awarded to Charles Booth in 1892. Only two statisticians, H. Cramer (Norwegian) and J. Neyman (Polish), outside Great Britain were awarded the Gold medal and C. R. Rao is the first non-European and non-American to receive the award. Other awards he has received are the Gold Medal of Calcutta University, Wilks Medal of the American Statistical Association, Wilks Army Medal, Guy Medal in Silver of the Royal Statistical Society (UK), Megnadh Saha Medal and Srinivasa Ramanujan Medal of the Indian National Science Academy, J.C.Bose Gold Medal of Bose Institute and Mahalanobis Centenary Gold Medal of the Indian Science Congress, the Bhatnagar award of the Council of Scientific and Industrial Research, India and the Government of India honored him with the second highest civilian award, Padma Vibhushan, for outstanding contributions to Science and Engineering / Statistics?, and also instituted a cash award in honor of C R Rao, to be given once in two years to a young statistician for work done during the preceding 3 years in any field of statistics. For his outstanding achievements Rao has been honored with the establishment of an institute named after him, C.R.Rao Advanced Institute for Mathematics, Statistics and Computer Science, in the campus of the University of Hyderabad, India. C.R. Rao won International Statistics Prize in 2023. He passed away in 2023 two weeks before his 103rd birthday.

Table of 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.

Additional information

NPB9780444820914
9780444820914
0444820914
Order Statistics: Theory and Methods: Volume 16 by Narayanaswamy Balakrishnan (Distinguished University Professor, Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada)
New
Hardback
Elsevier Science & Technology
1998-07-09
752
N/A
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