Projecting Statistical Functionals : LECTURE NOTES IN STATISTICS - Tomasz Rychlik

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Projecting Statistical Functionals

By: Tomasz Rychlik

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Paperback | 1 December 2000

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192 Pages

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23.39 x 15.6 x 1.04

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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.

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Preface
List of Tables
Introduction and Notation	p. 1
Basic Notions	p. 11
Quantiles	p. 33
Order Statistics of Independent Samples	p. 55
Order Statistics of Dependent Observations	p. 95
Records and [kappa]th Records	p. 131
Predictions of Order and Record Statistics	p. 145
Further Research Directions	p. 157
References	p. 163
Author Index	p. 171
Subject Index	p. 173
Table of Contents provided by Blackwell. All Rights Reserved.

Projecting Statistical Functionals

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Paperback

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