Robust statistical methods / William J. J. Rey

This monograph consolidates results from the literature on robust statistical estimation and presents some original material. Topics include: (i) sampling distribution theory for robust estimation, with special emphasis on a Taylor-like expansion in terms of von Mises derivatives; (ii) the jackknife method, discussed in the context of the Taylor-like expansion; (iii) M-estimation and its generalization to a method, called MM-estimation, for simultaneously estimating interdependent parameters. An appendix presents more details on especially important concepts, such as distribution spaces, the Prohorov metric, a definition of the term robust, and the influence function. The important topics of L-estimation and R-estimation are not discussed.
The text is rife with misprints and/or errors, both in the mathematics and in the English. The errors sometimes occur at crucial places. The book contains many conjectures and speculations and lacks mathematical rigour. For example, Taylor-like expansions play an important role, but all such expansions are written so as to end with dot-dot-dot; neither a remainder term nor a statement concerning convergence is presented. The author does warn the reader that sometimes "a strict demonstration has not been possible''.
This is clearly not the first book one should read to learn something about robust estimation. Perhaps there are enough good, original ideas hidden in this abstract, ambiguous presentation to merit the attention of experts in the field, but the search for those pearls will not be easy. (MathSciNet)