Robustness in data analysis
Subtitle: criteria and methods
By: Georgy L. Shevlyakov and Nikita O. Vilchevski.
Contributors: Vilʹchevskiĭ, N. O.
Series: Modern probability and statistics,
Publisher: VSP
Published: 2002
Place of publication: Utrecht; Boston
Language: eng
Number of pages: 310
Subjects: Robust statistics.; Mathematical statistics.
Notes: Includes bibliographical references (p. 291-308) and index.
Table of contents: value: Machine generated contents note: 1 Introduction; value: 1.1 General remarks; value: 1.2 Huber minimax approach; value: 1.3 Hampel approach; value: 2 Optimization criteria in data analysis: a probability-free approach; value: 2.1 Introductory remarks; value: 2.2 Translation and scale equivariant contrast functions; value: 2.3 Orthogonal equivariant contrast functions; value: 2.4 Monotonically equivariant contrast functions; value: 2.5 Minimal sensitivity to small perturbations in the data; value: 2.6 Affine equivariant contrast functions; value: 3 Robust minimax estimation of location; value: 3.1 Introductory remarks; value: 3.2 Robust estimation of location in models with bounded variances; value: 3.3 Robust estimation of location in models with bounded subranges; value: 3.4 Robust estimators of multivariate location; value: 3.5 Least informative lattice distributions; value: 4 Robust estimation of scale; value: 4.1 Introductory remarks; value: 4.2 Measures of scale defined by functionals; value: 4.3 M-,L-, and R-estimators of scale; value: 4.4 Huber minimax estimator of scale; value: 4.5 Final remarks; value: 5 Robust regression and autoregression; value: 5.1 Introductory remarks; value: 5.2 The minimax variance regression; value: 5.3 Robust autoregression; value: 5.4 Robust identification in dynamic models; value: 5.5 Final remarks; value: 6 Robustness of Ll-norm estimators; value: 6.1 Introductory remarks; value: 6.2 Stability of Ll-approximations; value: 6.3 Robustness of the Ll-regression; value: 6.4 Final remarks; value: 7 Robust estimation of correlation; value: 7.1 Introductory remarks; value: 7.2 Analysis: Monte Carlo experiment; value: 7.3 Analysis: asymptotic characteristics; value: 7.4 Synthesis: minimax variance correlation; value: 7.5 Two-stage estimators: rejection of outliers plus classics; value: 8 Computation and data analysis technologies; value: 8.1 Introductory remarks on computation; value: 8.2 Adaptive robust procedures; value: 8.3 Smoothing quantile functions by the Bernstein polynomials; value: 8.4 Robust bivariate boxplots; value: 9 Applications; value: 9.1 On robust estimation in the statistical theory of reliability; value: 9.2 Robust detection of signals based on optimization criteria; value: 9.3 Statistical analysis of sudden cardiac death risk factors.