Robustness in Data Analysis: criteria and methods
Criteria and Methods
1st Edition
Published on 20. December 2001
Book
Hardback
310 pages
978-90-6764-351-1 (ISBN)
Description
01/07 This title is now available from Walter de Gruyter. Please see www.degruyter.com for more information.
The field of mathematical statistics called robustness statistics deals with the stability of statistical inference under variations of accepted distribution models. Although robust statistics involves mathematically highly defined tools, robust methods exhibit a satisfactory behaviour in small samples, thus being quite useful in applications.
This volume in the book series Modern Probability and Statistics addresses various topics in the field of robust statistics and data analysis, such as: a probability-free approach in data analysis; minimax variance estimators of location, scale, regression, autoregression and correlation; L1-norm methods; adaptive, data reduction, bivariate boxplot, and multivariate outlier detection algorithms; applications in reliability, detection of signals, and analysis of the sudden cardiac death risk factors.
The book contains new results related to robustness and data analysis technologies, including both theoretical aspects and practical needs of data processing, which have been relatively inaccessible as they were originally only published in Russian.
This book will be of value and interest to researchers in mathematical statistics as well as to those using statistical methods.
The field of mathematical statistics called robustness statistics deals with the stability of statistical inference under variations of accepted distribution models. Although robust statistics involves mathematically highly defined tools, robust methods exhibit a satisfactory behaviour in small samples, thus being quite useful in applications.
This volume in the book series Modern Probability and Statistics addresses various topics in the field of robust statistics and data analysis, such as: a probability-free approach in data analysis; minimax variance estimators of location, scale, regression, autoregression and correlation; L1-norm methods; adaptive, data reduction, bivariate boxplot, and multivariate outlier detection algorithms; applications in reliability, detection of signals, and analysis of the sudden cardiac death risk factors.
The book contains new results related to robustness and data analysis technologies, including both theoretical aspects and practical needs of data processing, which have been relatively inaccessible as they were originally only published in Russian.
This book will be of value and interest to researchers in mathematical statistics as well as to those using statistical methods.
More details
Series
Edition
Reprint 2012
Language
English
Place of publication
Zeist
Netherlands
Publishing group
Brill
Target group
College/higher education
Professional and scholarly
US School Grade: College Graduate Student
Product notice
Laminated cover
Dimensions
Height: 249 mm
Width: 165 mm
Weight
650 gr
ISBN-13
978-90-6764-351-1 (9789067643511)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
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Additional editions
E-Book
12/2011
1st Edition
De Gruyter
€209.00
Available for download
Book
01/2001
1st Edition
De Gruyter
€309.00
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Content
Introduction
General remarks; Huber minimax approach; Hampel approach
Optimization criteria in data analysis: a probability-free approach
Introductory remarks; Translation and scale equivariant contrast functions; Orthogonal equivariant contrast functions; Monotonically equivariant contrast functions; Minimal sensitivity to small perturbations in the data; Affine equivariate contrast functions
Robust mimimax estimation of location
Introductory remarks; Robust estimation of location in models with bounded variances; Robust estimation of location in models with bounded subranges; Robust estimators of multivariate location; Least informative lattice distributions
Robust estimation of scale
Introductory remarks; Measures of scale defined by functionals; M-, L-, and R-estimators of scale; Huber minimax estimator of scale; Final remarks
Robust regression and autoregression
Introductory remarks; The minimax variance regression; Robust autoregression; Robust identification in dynamic models; Final remarks
Robustness of L1-norm estimators
Introductory remarks; Stability of L1-approximations; Robustness of the L1-regression; Final remarks
Robust estimation of correlation
Introductory remarks; Analysis: Monte Carlo experiment; Analysis: asymptotic characteristics; Synthesis; minimax variance correlation; Two-stage estimators: rejection of outliers plus classics
Computation and data analysis technologies
Introductory remarks on computation; Adaptive robust procedures; Smoothing quantile functions by the Bernstein polynomials; Robust bivariate boxplots
Applications
On robust elimination in the statistical theory of reliability; Robust detection of signals based on optimisation criteria; Statistical analysis of sudden cardiac death risk factors
Bibliography; Index
General remarks; Huber minimax approach; Hampel approach
Optimization criteria in data analysis: a probability-free approach
Introductory remarks; Translation and scale equivariant contrast functions; Orthogonal equivariant contrast functions; Monotonically equivariant contrast functions; Minimal sensitivity to small perturbations in the data; Affine equivariate contrast functions
Robust mimimax estimation of location
Introductory remarks; Robust estimation of location in models with bounded variances; Robust estimation of location in models with bounded subranges; Robust estimators of multivariate location; Least informative lattice distributions
Robust estimation of scale
Introductory remarks; Measures of scale defined by functionals; M-, L-, and R-estimators of scale; Huber minimax estimator of scale; Final remarks
Robust regression and autoregression
Introductory remarks; The minimax variance regression; Robust autoregression; Robust identification in dynamic models; Final remarks
Robustness of L1-norm estimators
Introductory remarks; Stability of L1-approximations; Robustness of the L1-regression; Final remarks
Robust estimation of correlation
Introductory remarks; Analysis: Monte Carlo experiment; Analysis: asymptotic characteristics; Synthesis; minimax variance correlation; Two-stage estimators: rejection of outliers plus classics
Computation and data analysis technologies
Introductory remarks on computation; Adaptive robust procedures; Smoothing quantile functions by the Bernstein polynomials; Robust bivariate boxplots
Applications
On robust elimination in the statistical theory of reliability; Robust detection of signals based on optimisation criteria; Statistical analysis of sudden cardiac death risk factors
Bibliography; Index