Robustness in data analysis : criteria and methods / Georgy L. Shevlyakov and Nikita O. Vilchevski.

Format:

Book

Author/Creator:

Shevlyakov, Georgy L.

Contributor:

Vilchevskii, N. O.

Series:

Modern Probability and Statistics

Modern probability and statistics, 1385-7738

Language:

English

Subjects (All):

Robust statistics.

Mathematical statistics.

Physical Description:

1 online resource (324 p.)

Edition:

Reprint 2012

Place of Publication:

Utrecht ; Boston : VSP, 2002.

Language Note:

English

Summary:

The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.

Contents:

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.

Notes:

Description based upon print version of record.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

Includes bibliographical references (p. 291-308) and index.

ISBN:

9783110936001

3110936003

OCLC:

979765888