Robust Statistics: The Approach Based on Influence Functions (Wiley Series in Probability and Statistics) [Hardcover]

Frank R. Hampel (Author), Elvezio M. Ronchetti (Author), Peter J. Rousseeuw (Author), Werner A. Stahel (Author)

Book Description

ISBN-10: 0471829218 | ISBN-13: 978-0471829218 | Publication Date: January 17, 1986 | Edition: 1

The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists.

"This is a nice book containing a wealth of information, much of it due to the authors. . . . If an instructor designing such a course wanted a textbook, this book would be the best choice available. . . . There are many stimulating exercises, and the book also contains an excellent index and an extensive list of references."
—Technometrics

"[This] book should be read carefully by anyone who is interested in dealing with statistical models in a realistic fashion."
—American Scientist

Introducing concepts, theory, and applications, Robust Statistics is accessible to a broad audience, avoiding allusions to high-powered mathematics while emphasizing ideas, heuristics, and background. The text covers the approach based on the influence function (the effect of an outlier on an estimater, for example) and related notions such as the breakdown point. It also treats the change-of-variance function, fundamental concepts and results in the framework of estimation of a single parameter, and applications to estimation of covariance matrices and regression parameters.

Editorial Reviews

From the Publisher

A highly detailed, yet readable treatment of the growing field of robust statistics--the statistics of approximate parametric models. Introducing concepts, theory, and applications, this work is designed to be accessible to a broad audience, avoiding allusions to high-powered mathematics while emphasizing ideas, heuristics, and background. It covers the approach based on the influence function (the effect of an outlier on an estimater, for example) and related notions such as the breakdown point. Also treats the change-of-variance function, fundamental concepts and results in the framework of estimation of a single parameter, and applications to estimation of covariance matrices and regression parameters.

From the Back Cover

The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists.

"This is a nice book containing a wealth of information, much of it due to the authors. . . . If an instructor designing such a course wanted a textbook, this book would be the best choice available. . . . There are many stimulating exercises, and the book also contains an excellent index and an extensive list of references."
—Technometrics

"[This] book should be read carefully by anyone who is interested in dealing with statistical models in a realistic fashion."
—American Scientist

Introducing concepts, theory, and applications, Robust Statistics is accessible to a broad audience, avoiding allusions to high-powered mathematics while emphasizing ideas, heuristics, and background. The text covers the approach based on the influence function (the effect of an outlier on an estimater, for example) and related notions such as the breakdown point. It also treats the change-of-variance function, fundamental concepts and results in the framework of estimation of a single parameter, and applications to estimation of covariance matrices and regression parameters. --This text refers to the Paperback edition.

See all Editorial Reviews

Product Details

• Hardcover: 528 pages
• Publisher: Wiley; 1 edition (January 17, 1986)
• Language: English
• ISBN-10: 0471829218
• ISBN-13: 978-0471829218
• Product Dimensions: 9.1 x 6.2 x 1.6 inches
• Shipping Weight: 2.2 pounds
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #2,516,247 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

28 of 29 people found the following review helpful:

5.0 out of 5 stars a Wiley classic, February 6, 2008

By 

Michael R. Chernick "statman31147" (Holland PA) - See all my reviews
(REAL NAME)   

This review is from: Robust Statistics: The Approach Based on Influence Functions (Wiley Series in Probability and Statistics) (Paperback)

This is an excellent by Hampel and his colleagues. Hampel in the 1970s introduced the concept of the influence function as a measure for assessing the robustness of an estimator. The influence function evaluated at a point x shows how much a single observed value of x affects or "influences" an estimator of a particular parameter. Hampel also derived analytic expressions for various influence functions since they could be evaluated as functional derivatives. Gnandesikan in his book on multivariate analysis derives the contours of constant value for the influence function for bivariate correlation. These contours are hyperbolic and indicate the directions in two dimensions where the influence of the two-dimensional point is the greatest.

In a paper that recieved the Wolfowitz Prize in 1983 I derived the influence function from multiple correlation and also show how in practiice the estimated influence function for bivariate correlation can be used to identify the directions to be most concerned about for outliers in data.

This book was first published in 1986 and it presents robust estimators obtained and evaluated using the influence function approach. While there are other approaches to obtain and evaluate robust statistics, I have always found the influence function approach to be the most intuitive and easiest to understand. I think it is also helpful in decining multivariate outliers where the direction to move in the n-dimensional space to find outliers is not obvious and clearly depends on what the parameter is that you are estimation.

Books in the Wiley series in probability and statistics are published in hardcover and can be rather expensive. The publisher has looked at its best sellers over the course of ten years or more and put those deignated books in their classic series. The book is then reissued in paperback at a substantially reduced price. So if you don't have this book getting the paperback efition is a real bargain.