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von Mises Calculus For Statistical Functionals (Lecture Notes in Statistics,...

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Specificaties

Objectstaat
Goed: Een boek dat is gelezen, maar zich in goede staat bevindt. De kaft is zeer minimaal beschadigd ...
Release Year
1983
Book Title
von Mises Calculus For Statistical Functionals (Lecture Notes ...
ISBN
9780387908991
Series
Lecture Notes in Statistics Ser.
Publication Year
1983
Type
Textbook
Format
Trade Paperback
Language
English
Publication Name
Von Mises Calculus for Statistical Functionals
Author
L. T. Fernholz
Item Length
9.3in
Publisher
Springer New York
Item Width
6.1in
Item Weight
7.7 Oz
Number of Pages
124 Pages

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Product Information

About forty years ago, Richard von Mises proposed a theory for the analysis of the asymptotic behavior of nonlinear statistical functionals based on the differentiability properties of these functionals. His theory was largely neglected until the late 1960's when it experienced a renaissance due to developments in the field of robust statistics. In particular, the "Volterra" derivative used by von Mises evolved into the influence curve, which was used to provide information about the sensi­ ti vity of an estimator to outliers, as well as the estimator's asymptot­ ic variance. Moreover, with the "Princeton Robustness Study" (Andrews et al. (1972)), there began a proliferation of new robust statistics, and the formal von Mises calculations provided a convenient heuristic tool for the analysis of the asymptotic distributions of these statistics. In the last few years, these calculations have been put in a more rigorous setting based on the Frechet and Hadamard, or compact, derivatives. The purpose of these notes is to provide von Mises' theory with a rig­ orous mathematical framework which is sufficiently straightforward so that it can be applied routinely with little more effort than is required for the calculation of the influence curve. The approach presented here is based on the Hadamard derivative and is applicable to diverse forms of sta­ tistical functionals.

Product Identifiers

Publisher
Springer New York
ISBN-10
0387908994
ISBN-13
9780387908991
eBay Product ID (ePID)
1954543

Product Key Features

Author
L. T. Fernholz
Publication Name
Von Mises Calculus for Statistical Functionals
Format
Trade Paperback
Language
English
Series
Lecture Notes in Statistics Ser.
Publication Year
1983
Type
Textbook
Number of Pages
124 Pages

Dimensions

Item Length
9.3in
Item Width
6.1in
Item Weight
7.7 Oz

Additional Product Features

Series Volume Number
19
Number of Volumes
1 Vol.
Lc Classification Number
Qa273.A1-274.9
Table of Content
I. Introduction.- II. Von Mises' Method.- 2.1 Statistical functionals.- 2.2 Von Mises expansions.- 2.3 Frééchet derivatives.- III. Hadamard Differentiation.- 3.1 Definitions of differentiability.- 3.2 An implicit function theorem.- IV. Some Probability Theory on C[0,1] and D[0,1].- 4.1 The spaces C[0,1] and D[0,1].- 4.2 Probability theory on C[0,1].- 4.3 Probability theory on D[0,1].- 4.4 Asymptotic Normality.- V. M-, L-, and R-Estimators.- 5.1 M-estimators.- 5.2 L-estimators.- 5.3 R-estimators.- 5.4 Modifications of elements of D[0,1].- VI. Calculus on Function Spaces.- 6.1 Differentiability theorems.- 6.2 An implicit function theorem for statistical functionals.- VII. Applications.- 7.1 M-estimators.- 7.2 L-estimators.- 7.3 R-estimators.- 7.4 Functionals on C[0,1]: sample quantiles.- 7.5 Truncated d.f.'s and modified estimators.- VIII. Asymptotic Efficiency.- 8.1 Asymptotic efficiency and Hadamard differentiability.- 8.2 Asymptotically efficient estimators of location.- References.- List of symbols.
Copyright Date
1983
Topic
Probability & Statistics / Stochastic Processes, Probability & Statistics / General, Applied
Intended Audience
Scholarly & Professional
Illustrated
Yes
Genre
Mathematics

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They put a barcode sticker that doesn't come off on the front of book, right over the title. Why?
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Didn't like the sticker on the face of the book. Other than that, thank you.