# Robust Statistics: The Approach Based on Influence Functions

This is a wonderful book about robust statistics. While it is an advanced one, it is not as advanced as Robust Statistics.

My favorite chapter is the first one: “Introduction and Motivation.” This is a 77-page read in which Hampel et al. set up the right mindset of using robust statistics. Just look at this picture from page 3 (click to enlarge):

The drawing is quite simple, but I feel so much love for the topic here. The authors had a valid option of writing a book without such illustrations (like most other mathematical books). But they deliberately decided to include such a picture in the book. The writing style is also quite friendly: sometimes it feels like a chat with a friend rather than like a mathematical textbook.

As you may guess from the title, the primary topic of the book is the influence functions. While these functions are discussed in most books on robust statistics, Frank R. Hampel is the person who introduced them. Unfortunately, not so many researchers nowadays actually use the influence functions to evaluate the properties of the selected estimators. I have to admit that this approach may be challenging to apply in some practical applications. If you, like me, do not always feel confident with using the influence functions, reading (or rereading) Hampel’s book is a great way to improve relevant skills!

Conclusion: the first chapter is recommended for everyone; the rest of the book is recommended for advanced readers.

## Reference

Frank R. Hampel, Elevezio M. Ronchetti, Peter J. Rousseeuw, Werner A. Stahel“Robust statistics: the approach based on influence functions” (1986) // Publisher: Wiley. New York. ISBN: 978-0-471-73577-9.

## Bib

```
@Book{hampel1986,
address = {New York},
edition = {Digital print},
series = {Wiley series in probability and mathematical statistics Probability and mathematical statistics},
title = {Robust statistics: the approach based on influence functions},
isbn = {978-0-471-73577-9},
shorttitle = {Robust statistics},
language = {eng},
publisher = {Wiley},
editor = {Hampel, Frank R. and Ronchetti, Elevezio M. and Rousseeuw, Peter J. and Stahel, Werner A.},
year = {1986}
}
```