Peter J.Huber – Robust Statistics

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.

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 ubject. The treatment here is theoretical, with the stress on concepts rather than on extensive mathematical completeness. 1 provides a general introduction and overview. 2 contains an account of the formal mathematical background behind qualitative and quantitative robustness. 3 introduces the M-, L-, and R-estimates, and Chapter 4 treats the asymptotic minimax theory for location estimates.