Projecting Statistical Functionals (Lecture Notes in Statistics, 160, Band 160) - Softcover

Rychlik, Tomasz

Softcover

ISBN 10: 038795239X ISBN 13: 9780387952390

Verlag: Springer New York, 2001

Inhaltsangabe

About 10 years ago I began studying evaluations of distributions of or­ der statistics from samples with general dependence structure. Analyzing in [78] deterministic inequalities for arbitrary linear combinations of order statistics expressed in terms of sample moments, I observed that we obtain the optimal bounds once we replace the vectors of original coefficients of the linear combinations by the respective Euclidean norm projections onto the convex cone of vectors with nondecreasing coordinates. I further veri­ fied that various optimal evaluations of order and record statistics, derived earlier by use of diverse techniques, may be expressed by means of projec­ tions. In Gajek and Rychlik [32], we formulated for the first time an idea of applying projections onto convex cones for determining accurate moment bounds on the expectations of order statistics. Also for the first time, we presented such evaluations for non parametric families of distributions dif­ ferent from families of arbitrary, symmetric, and nonnegative distributions. We realized that this approach makes it possible to evaluate various func­ tionals of great importance in applied probability and statistics in different restricted families of distributions. The purpose of this monograph is to present the method of using pro­ jections of elements of functional Hilbert spaces onto convex cones for es­ tablishing optimal mean-variance bounds of statistical functionals, and its wide range of applications. This is intended for students, researchers, and practitioners in probability, statistics, and reliability.

Über diesen Titel

Über die Autorin bzw. den Autor

Professor N. Balakrishnan is a Distinguished University Professor in the Department of Mathematics and Statistics at McMaster University, Hamilton, Canada. He is a Fellow of the Royal Society of Canada, a Fellow of the American Statistical Association, a Fellow of the Institute of Mathematical Statistics, and a recipient of an honorary doctoral degree from the National and Kapodistrian University of Athens, Greece. He is an author of many well-known books and research monographs in Statistics including the well-known four encyclopedic volumes on Statistical Distributions published by John Wiley & Sons. He is currently the Editor-in-Chief of three series of Communications in Statistics as well as Mathematical Methods of Statistics. Professor Tomasz Rychlik received the M.Sc. Degree in applied mathematics at the Faculty of Applied Mathematics and Technical Physics of the Technical University of Warsaw, Poland, in 1982. He defended his PhD thesis on robust statistics at the Institute of Mathematics, Polish Academy of Sciences in 1986. Now he is Professor of Mathematics at the Institute of Mathematics, Polish Academy of Sciences. His research interests contain probabilistic inequalities, reliability theory, and stochastic orders. He has published over 120 papers. Most of them were devoted to inequalities for ordered random variables.

Details zur Ausgabe

• Verlag: Springer New York
• Erscheinungsdatum: 2001
• Sprache: Englisch
• ISBN 10: 038795239X
• ISBN 13: 9780387952390
• Einband: Taschenbuch
• Anzahl der Seiten: 192
• Kontakt zum Hersteller: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Deutschland