Abstrakt
The methodology presented in the book demonstrates the way for further developments on robust and nonprametric procedures in more complex statistical models. Using examples to illustrate the methods, the text highlights applications in biomedical science, bioinformatics, finance and engineering.
Among others, it presents multivariate robust and nonparametric estimation with special emphasis on affine-equivariant procedures, followed by hypotheses testing and confidence sets. It keeps mathematical abstractions in a reasonable exent, while remaining largely theoretical.
Chapter 1: Introduction. Ch. 2: Preliminaries; Inference in linear models; Robustness concepts;Robust and minimax estimation of location; Clippings from probability and asymptotic theory.
Ch. 3: Robust Estimation of Location and Regression; M-estimators; L-estimators; R-estimators; Minimum distance and Pitman estimators;Differentiable statistical functions. Ch. 4: Asymptotic Representations for L-Estimators.
Ch. 5: Asymptotic Representations for M-Estimators. Ch 6: Asymptotic Representations for R-Estimators.
Ch. 7: Asymptotic Interrelations of Estimators. Ch. 8: Robust Estimation: Multivariate Perspectives.
Ch 9. Robust Tests and Confidence Sets.