Robust Statistics

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.Huber, Peter J. is the author of 'Robust Statistics' with ISBN 9780471418054 and ISBN 0471418056.