Projecting Statistical Functionals by Tomasz RychlikProjecting Statistical Functionals by Tomasz Rychlik

Projecting Statistical Functionals

byTomasz Rychlik

Paperback | April 20, 2001

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This monograph presents a general method of establishing explicit solutions to classical problems of calculating the best lower and upper mean-variance bounds on various statistical functionals over various nonparametric families of distributions. The functionals include quantiles, standard and conditional expectations of record and order statistics from independent and dependent samples, and a variety of their combinations important in statistics and reliability. The following families of distributions are taken into account: arbitrary, symmetric, symmetric unimodal, and U-shaped ones, distributions with monotone density and failure rate, and monotone density and failure rate on the average distributions. The method is based on determining projections of the functionals onto properly chosen convex cones in functional Hilbert spaces. It allows us to explicitly point out the distributions which attain the bounds. The book is addressed to students, researchers, and practitioners in statistics and applied probability. Most of the results have been established recently, and a significant part of them has not been published yet. Numerous open problems are stated in the text.
Title:Projecting Statistical FunctionalsFormat:PaperbackDimensions:184 pages, 9.25 × 6.1 × 0.07 inPublished:April 20, 2001Publisher:Springer New YorkLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:038795239X

ISBN - 13:9780387952390

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Table of Contents

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