Introduction to Robust Estimation and Hypothesis Testing

The topic of robust statistics claims to be practical. However, the three previous books may look too theoretical. While they discuss how to adapt mathematical tools to bizarre real-life data, they are too focused on the theoretical aspects of the suggested approaches. Sometimes, another reading session of another chapter leaves me in a confusing state. I think: “OK, all of this sounds fascinating and marvelous, but how do I solve my particular problem? Which method/approach/estimator/etc should I choose?”

At this moment, I open “Introduction to Robust Estimation and Hypothesis Testing” by Rand R. Wilcox. This is the most practical book about robust statistics. The theoretical part is reduced to the minimum: only the essential equations are presented. Instead of presenting the advanced stuff, references to relevant books and papers are provided. Such a format may be challenging for beginners: the knowledge of theoretical basis significantly simplifies the reading process.

However, if you know the basics, this is a wonderful handbook. It contains a broad overview of robust statistical tools. And it is not just a plain enumeration. For me, the most precious feature of this book is a plethora of small remarks regarding the real-life experience of suggested approaches. What kinds of pitfalls should we expect, what are the corner cases, which estimator is more efficient and when, and so on. The second most precious feature of this book is a set of reference R implementations for almost all the presented methods. If I’m curious about the actual behavior of the suggested estimator, I should not spend time implementing it from scratch: I can just take the ready implementation and start my experiments. In most cases, I use this book to get a brief overview of available approaches for the task I am working on.

Conclusion: recommended to engineers who are using robust statistics in real life.

Excerpts

To begin, distributions are never normal. For some this seems obvious, hardly worth mentioning, but an aphorism given by Cramér (1946) and attributed to the mathematician Poincaré remains relevant: “Everyone believes in the [normal] law of errors, the experimenters because they think it is a mathematical theorem, the mathematicians because they think it is an experimental fact.”