Robust Statistics

Other volumes in the Wiley Series in Probability and Mathematical Statistics Abstract Inference UIf Grenander The traditional setting of statistical inference is when both sample space and parameter space are finite dimensional Euclidean spaces or subjects of such spaces. During the last decades, however, a theory has been developed that allows the sample space to be some abstract space. More recently, mathematical techniques—especially the method of sieves—have been constructed to enable inferences to be made in abstract parameter spaces. This work began with the author’s 1950 monograph on inference in stochastic processes (for general sample space) and with the sieve methodology (for general parameter space) that the author and his co-workers at Brown University developed in the 1970s. Both of these cases are studied in this volume, which is the first comprehensive treatment of the subject. 1980 Order Statistics, 2nd Ed. Herbert A. David Presents up-to-date coverage of the theory and applications of ordered random variables and their functions. Develops the distribution theory of order statistics systematically, and treats short-cut methods, robust estimation, life testing, reliability, and extreme-value theory. Applications include procedures for the treatment of outliers and other data analysis techniques. Provides extensive references to the literature and the tables contained therein. Exercises included. 1980 Theory and Applications of Stochastic Differential Equations Zeev Schuss Presents SDE theory through its applications in the physical sciences, e.g., the description of chemical reactions, solid state diffusion and electrical conductivity, population genetics, filtering problems in communication theory, etc. Introduces the stochastic calculus in a simple way, presupposing only basic analysis and probability theory. Shows the role of first passage times and exit distributions in modeling physical phenomena. Introduces analytical methods in order to obtain information on probabilistic quantities such as moments and distribution of first passage times and transition probabilities, and demonstrates the role of partial differential equations. Methods include singular perturbation techniques, old and new asymptotic methods, and boundary layer theory. 1980