Peter J. Huber
CBMS-NSF Regional Conference Series in Applied Mathematics 68
Here is a brief, well-organized, and easy-to-follow introduction and overview of robust statistics. Huber focuses primarily on the important and clearly understood case of distribution robustness, where the shape of the true underlying distribution deviates slightly from the assumed model (usually the Gaussian law). An additional chapter on recent developments in robustness has been added and the reference list has been expanded and updated from the 1977 edition.
This book provides a quick introduction to robustness. Graduate and undergraduate students in statistics will find it especially useful.
Preface to the Second Edition; Preface to the First Edition; Chapter 1: Background. Why robust procedures?; Chapter 2: Qualitative and Quantitative Robustness. Qualitative robustness; Quantitative robustness, breakdown; Infinitesimal robustness, influence function; Chapter 3: M-,L-, and R-Estimates. M-estimates; L-estimates; R-estimates; Asymptotic properties of M-estimates; Asymptotically efficient M-, L-, R-estimates; Scaling question; Chapter 4: Asymptotic Minimax Theory. Minimax asymptotic bias; Minimax asymptotic variance; Chapter 5: Multiparameter Problems. Generalities; Regression; Robust covariances: the affinely invariant case; Robust covariances: the coordinate dependent case; Chapter 6: Finite Sample Minimax Theory. Robust tests and capacities; Finite sample minimax estimation; Chapter 7: Adaptive Estimates. Adaptive estimates; Chapter 8: Robustness: Where are We Now? The first ten years; Influence functions and psuedovalues; Breakdown and outlier detection; Studentizing; Shrinking neighborhoods; Design; Regression; Multivariate problems; Some persistent misunderstandings; Future directions; References.
1996 / x + 67 pages / Softcover / ISBN-13: 978-0-898713-79-4 / ISBN-10: 0-89871-379-X /
List Price $39.00 / SIAM/CBMS Member Price $27.30 / Order Code CB68