Springer Robust Asymptotic Statistics: Volume I (Springer Series in Statistics)

This volume gives a rigorous account of the asymptotic theory of robust statistics, from the viewpoint of optimally robust functionals and their unbiased estimators and tests. By linking up the local asymptotic minimax criterion with further optimality, the author creates a powerful and unifying notion of robustness. Consequently, this volume gives a self-contained treatment of the main optimality results of asymptotic statistics, and supplies the necessary tools of convex optimization and weak convergence. The volume is an ideal reference for researchers who work in statistics and graduate students with a basic knowledge of probability and statistics. Some of the main topics covered are: von Mises functionals, log-likelihoods, asymptotic statistics, nonparametric statistics, optimal influence curves, the constructional problem, and robust regression.