A Study of the Theory and Application of Robustness in Statistics

What is it about?

This work is a combination of historical and current views in robust statistics with new material on consistency in the face of estimating equations when there are multiple roots and also on the L2- minimum distance estimation when estimating parameters in mixture modelling. In particular the subject of switching regressions is investigated for the L2-minimum distance estimator. The classical theory of M-estimation is reviewed with respect to weakly continuous and Frechet differentiable statistical functionals. The book begins with estimation of location and scale and continues with regression estimation. The latter part of the book deals with adaptive estimation and outlier detection, for location, regression and multivariate data. There is also some new work on small sample bias corrections.

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Why is it important?

The book is important as it gives a historical account of much of the author's work, including applications of the theory on weak continuity and Frechet differentiability in real settings. It also gives a recent view of the study of outliers in multiple regression and in multivariate settings where the interest can be in identifying the outliers. The link between consistency and the theory of uniform convergence helps elucidate the many facets of M-estimators which include maximum likelihood estimators. Therefore the application is broad.

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