Robust Statistics (Wiley Series in Probability and Statistics) - Hardcover

Huber, Peter J.

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9780471418054: Robust Statistics (Wiley Series in Probability and Statistics)

Hardcover

ISBN 10: 0471418056 ISBN 13: 9780471418054

Publisher: Wiley-Interscience, 1981

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The first systematic, book-length treatment of the subject. Begins with a general introduction and the formal mathematical background behind qualitative and quantitative robustness. Stresses concepts. Provides selected numerical algorithms for computing robust estimates, as well as convergence proofs. Tables contain quantitative robustness information for a variety of estimates.

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From the Back Cover:

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

From the Inside Flap:

Although several leading scientists in the late nineteenth and early twentieth centuries possessed a clear, operational understanding of the idea of robust statistics, the field was not recognized as a legitimate area of investigation until the mid-1960s. Briefly, a statistical method that exhibits an insensitivity to deviation from its own assumptions, is robust. The present volume represents the first systematic, book-length exposition of the subject. The treatment here is theoretical, with the stress on concepts rather than on extensive mathematical completeness. Chapter 1 provides a general introduction and overview. Chapter 2 contains an account of the formal mathematical background behind qualitative and quantitative robustness. Chapter 3 introduces the M-, L-, and R-estimates, and Chapter 4 treats the asymptotic minimax theory for location estimates. Chapters 5 to 11 branch out in different directions and are basically self-contained, covering scale estimates, multiparameter problems, regression, robust covariance and correlation matrices, robustness of design, exact finite sample results, and miscellaneous topics. The text describes selected numerical algorithms for computing robust estimates, provides convergence proofs where possible, and includes numerous tables with quantitative robustness information for a variety of estimates. Robust Statistics reorganizes, summarizes and extends a wealth of material only partially available in published form, providing a solid foundation in robustness for statisticians, mathematicians and graduate students.

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