Methodology in Robust and Nonparametric Statistics

Jure?ková, Jana; Sen, Pranab; Picek, Jan

"... a useful addition to the present theoretical literature on robust methods ..." -David E. Booth, Technometrics, November 2014 "... this book is very detailed and offers many ingenious ways to set up expansions for robust estimators leading to asymptotic properties of statistics. In view of the broadness of the study undertaken over a number of years, there is something for everyone. ... To help the reader assimilate the ideas, there are ample problems at the end of each chapter." -Brenton R. Clarke, Australian & New Zealand Journal of Statistics, 2014 "There were several ideas that are rarely presented in other texts, but that I found of special interest. Many of these appear in the extended material on rank tests and functionals, and I found the development of rank tests from the regression quantile dual to be especially fruitful and elegant. ... I have always found that mathematical results are the hardest part of statistics to learn (or to teach), and that the best way to do this is through a clear and very systematic development with a careful balance between breadth and conceptual simplicity. This text provides just such an approach for the area of robust statistics." -Stephen Portnoy, Journal of the American Statistical Association, September 2013 "In summary, this book is mathematically rigorous with emphasis on the asymptotic theory of robust statistical inference. It is an excellent book for more mathematically oriented readers who intend to do further study in the field. For practitioners in the pharmaceutical industry, a solid theoretical background in mathematics and statistics is needed in order to gain a thorough understanding of the topics covered." -Journal of Biopharmaceutical Statistics

• Introduction and Synopsis. Preliminaries. Robust Estimation of Location and Regression. Asymptotic Representations for L-Estimators. Asymptotic Representations for M-Estimators. Asymptotic Representations for R-Estimators. Asymptotic Interrelations of Estimators. Robust Estimation: Multivariate Perspectives. Robust Tests and Confidence Sets. Robust Estimation: Multivariate Perspectives. Robust Tests and Confidence Sets.