Robustness in data analysis: criteria and methods/
Shevlyakov, Georgy L.
Robustness in data analysis: criteria and methods/ Georgy L. Shevlyakov and Nikita O. Vilchevski. - Utrecht ; Boston : VSP, 2002. - viii, 310 p. : ill. ; 25 cm.
Includes bibliographical references (p. 291-308) and index.
Machine generated contents note: 1 Introduction -- 1.1 General remarks-- 1.2 Huber minimax approach-- 1.3 Hampel approach-- 2 Optimization criteria in data analysis: a probability-free approach -- 2.1 Introductory remarks-- 2.2 Translation and scale equivariant contrast functions-- 2.3 Orthogonal equivariant contrast functions-- 2.4 Monotonically equivariant contrast functions-- 2.5 Minimal sensitivity to small perturbations in the data-- 2.6 Affine equivariant contrast functions-- 3 Robust minimax estimation of location -- 3.1 Introductory remarks-- 3.2 Robust estimation of location in models with bounded variances-- 3.3 Robust estimation of location in models with bounded subranges-- 3.4 Robust estimators of multivariate location-- 3.5 Least informative lattice distributions-- 4 Robust estimation of scale -- 4.1 Introductory remarks-- 4.2 Measures of scale defined by functionals-- 4.3 M-,L-, and R-estimators of scale-- 4.4 Huber minimax estimator of scale-- 4.5 Final remarks-- 5 Robust regression and autoregression -- 5.1 Introductory remarks-- 5.2 The minimax variance regression-- 5.3 Robust autoregression-- 5.4 Robust identification in dynamic models-- 5.5 Final remarks-- 6 Robustness of Ll-norm estimators -- 6.1 Introductory remarks-- 6.2 Stability of Ll-approximations-- 6.3 Robustness of the Ll-regression-- 6.4 Final remarks-- 7 Robust estimation of correlation -- 7.1 Introductory remarks-- 7.2 Analysis: Monte Carlo experiment-- 7.3 Analysis: asymptotic characteristics-- 7.4 Synthesis: minimax variance correlation-- 7.5 Two-stage estimators: rejection of outliers plus classics-- 8 Computation and data analysis technologies -- 8.1 Introductory remarks on computation-- 8.2 Adaptive robust procedures-- 8.3 Smoothing quantile functions by the Bernstein polynomials-- 8.4 Robust bivariate boxplots-- 9 Applications -- 9.1 On robust estimation in the statistical theory of reliability-- 9.2 Robust detection of signals based on optimization criteria-- 9.3 Statistical analysis of sudden cardiac death risk factors.
9067643513
Robust statistics.
Mathematical statistics.
519.5 / SHE/M
Robustness in data analysis: criteria and methods/ Georgy L. Shevlyakov and Nikita O. Vilchevski. - Utrecht ; Boston : VSP, 2002. - viii, 310 p. : ill. ; 25 cm.
Includes bibliographical references (p. 291-308) and index.
Machine generated contents note: 1 Introduction -- 1.1 General remarks-- 1.2 Huber minimax approach-- 1.3 Hampel approach-- 2 Optimization criteria in data analysis: a probability-free approach -- 2.1 Introductory remarks-- 2.2 Translation and scale equivariant contrast functions-- 2.3 Orthogonal equivariant contrast functions-- 2.4 Monotonically equivariant contrast functions-- 2.5 Minimal sensitivity to small perturbations in the data-- 2.6 Affine equivariant contrast functions-- 3 Robust minimax estimation of location -- 3.1 Introductory remarks-- 3.2 Robust estimation of location in models with bounded variances-- 3.3 Robust estimation of location in models with bounded subranges-- 3.4 Robust estimators of multivariate location-- 3.5 Least informative lattice distributions-- 4 Robust estimation of scale -- 4.1 Introductory remarks-- 4.2 Measures of scale defined by functionals-- 4.3 M-,L-, and R-estimators of scale-- 4.4 Huber minimax estimator of scale-- 4.5 Final remarks-- 5 Robust regression and autoregression -- 5.1 Introductory remarks-- 5.2 The minimax variance regression-- 5.3 Robust autoregression-- 5.4 Robust identification in dynamic models-- 5.5 Final remarks-- 6 Robustness of Ll-norm estimators -- 6.1 Introductory remarks-- 6.2 Stability of Ll-approximations-- 6.3 Robustness of the Ll-regression-- 6.4 Final remarks-- 7 Robust estimation of correlation -- 7.1 Introductory remarks-- 7.2 Analysis: Monte Carlo experiment-- 7.3 Analysis: asymptotic characteristics-- 7.4 Synthesis: minimax variance correlation-- 7.5 Two-stage estimators: rejection of outliers plus classics-- 8 Computation and data analysis technologies -- 8.1 Introductory remarks on computation-- 8.2 Adaptive robust procedures-- 8.3 Smoothing quantile functions by the Bernstein polynomials-- 8.4 Robust bivariate boxplots-- 9 Applications -- 9.1 On robust estimation in the statistical theory of reliability-- 9.2 Robust detection of signals based on optimization criteria-- 9.3 Statistical analysis of sudden cardiac death risk factors.
9067643513
Robust statistics.
Mathematical statistics.
519.5 / SHE/M