Customer Reviews

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

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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.