Methodology in Robust and Nonparametric Statistics

摘要

Beyond very special parametric models, finite sample distributional properties are next to impossible to develop. Since the area of robust statistics insists on considering alternatives to parametric models, asymptotic distribution theory becomes essential. This book is an updating and rewriting of the earlier text by the first two authors (Jureckova and Sen 1996), and it aims to provide graduate students with a systematic development of asymptotic theory for classical robust and nonparametric procedures. As a consequence, the book presupposes a moderately strong mathematical background, with knowledge of mathematical statistics at the level of the text by Lehmann and Casella (1998) or higher. While Chapter 2 provides a brief introduction to measure-theoretical probability theory, a formal course in this subject would be valuable. The exclusive focus on asymptotics leaves little room for issues like data analysis and computation. Nonetheless, what the book does provide is a relatively accessible and systematic treatment developing the mathematical and probabilistic tools needed to prove theorems about asymptotics for the classical L-, M-, and R-estimators. Since most other books on robustness (Maronna, Martin, and Yohai 2006; Huber and Ronchetti 2009; Wilcox 2011, among others) treat theory in detail only in the simplest case (M-estimation), this is a very useful text.