Projecting Statistical Functionals

Tomasz Rychlik

ISBN 10: 038795239X / ISBN 13: 9780387952390

Editore: Springer New York, Springer New York Apr 2001, 2001

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This item is printed on demand - Print on Demand Titel. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 192 pp. Englisch.

Codice articolo 9780387952390

Dati bibliografici

• Titolo: Projecting Statistical Functionals
• Editore: Springer New York, Springer New York Apr 2001
• Data di pubblicazione: 2001
• Lingua: Inglese
• ISBN 10: 038795239X
• ISBN 13: 9780387952390
• Rilegatura: Taschenbuch
• Condizione: Neu

Descrizione articolo

Riassunto

This book presents a method of establishing explicit solutions to classical problems of calculating the best lower and upper mean-variance bounds. The following families of distributions are taken into account: arbitrary, symmetric, symmetric unimodal, and U-shaped. The book is addressed to students, researchers, and practitioners in statistics and applied probability. Most of the results are recent, and a significant part of them has not been published yet. Numerous open problems are stated in the text.

Contenuti

Introduction and notation * Basic Notions * Quantiles * Order statistics of independent samples * Order statistics of dependent observations * Records and kth records * Predictions of order and record statistics * Further research directions