Robust Statistics, 2nd Edition

Preface

It has now been eleven years since the publication of the first edition of Robust Statistics: Theory and Methods in 2006. Since that time, there have been two developments prompting the need for a second edition. The first development is that since 2006 a number of new results in the theory and methods of robust statistics have been developed and published, in particular by the book's authors. The second development is that the S‐PLUS software has been superseded by the open source package R, so our original of the S‐PLUS robust statistics package became outdated. Thus, for this second edition, we have created a new R‐based package called RobStatTM, and in that package and at the publisher's web site we provide scripts for computing all the examples in the book.

We will now discuss the main research advances included in this second edition.

Finite‐sample robustness

Asymptotically normal robust estimators have tuning constants that allow users to control their normal distribution variance efficiency, in a trade‐off with robustness toward fat‐tailed non‐normal distributions. The resulting finite‐sample performance in terms of mean‐squared error (MSE), which takes into account bias as well as variance, can be considerably worse than implied by the asymptotic performance. This second edition contains useful new results concerning the finite‐sample MSE performance of robust linear regression and robust covariance estimators. These are briefly described below.

Linear regression ...