Journal ArticleDOI
Robust Procedures in Multivariate Analysis I: Robust Covariance Estimation
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In this article, the detection of atypical observations from multivariate data sets can be enhanced by examining probabilityplotsofMahalanobis squared distances using robust M-estimates of means and of covariances, rather than the usual maximum likelihood estimates.Abstract:
SUMMARY The detection of atypical observations from multivariate data sets can be enhanced by examining probabilityplotsofMahalanobis squared distances using robust M-estimates of means and of covariances, rather than the usual maximum likelihood estimates The weights associated with the robust estimation can also be used to indicate atypical observations For uncontaminated data, the robust estimates are similar to the usual estimates A procedure for robust principal component analysis is given; it also indicates atypical observations and provides an analysis relatively little influenced by such observationsread more
Citations
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Journal ArticleDOI
Unmasking Multivariate Outliers and Leverage Points
TL;DR: This work proposes to compute distances based on very robust estimates of location and covariance, better suited to expose the outliers in a multivariate point cloud, to avoid the masking effect.
Journal ArticleDOI
A general methodology for bootstrapping in non-parametric frontier models
Leâ Opold Simar,Paul W. Wilson +1 more
TL;DR: This paper proposes a general methodology for bootstrapping in frontier models, extending the more restrictive method proposed in Simar & Wilson (1998) by allowing for heterogeneity in the structure of efficiency.
Journal ArticleDOI
ROBPCA: A New Approach to Robust Principal Component Analysis
TL;DR: The ROBPCA approach, which combines projection pursuit ideas with robust scatter matrix estimation, yields more accurate estimates at noncontaminated datasets and more robust estimates at contaminated data.
Journal ArticleDOI
Identifying Multiple Outliers in Multivariate Data
TL;DR: In this article, the authors propose a procedure for the detection of multiple outliers in multivariate data, where the data set is first ordered using an appropriately chosen robust measure of outlyingness, and then the data sets are divided into two initial subsets: a "basic" subset which contains p + 1 "good" observations and a "nonbasic" subsets which contain the remaining n -p -1 observations.
Journal ArticleDOI
On the unification of line processes, outlier rejection, and robust statistics with applications in early vision
TL;DR: It is shown how prior assumptions about the spatial structure of outliers can be expressed as constraints on the recovered analog outlier processes and how traditional continuation methods can be extended to the explicit outlier-process formulation.
References
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Journal ArticleDOI
The Influence Curve and Its Role in Robust Estimation
TL;DR: In this article, the first derivative of an estimator viewed as functional and the ways in which it can be used to study local robustness properties are discussed, and a theory of robust estimation "near" strict parametric models is briefly sketched and applied to some classical situations.
Journal ArticleDOI
Robust $M$-Estimators of Multivariate Location and Scatter
TL;DR: In this article, the robust estimation of the location vector and scatter matrix by means of "$M$-estimators," defined as solutions of the system: √ √ u_1(d_i)(\math{x}_i - \mathbf{t}) = \mathBF{0}$ and $n^{-1]-sum_i u_2(d-i^2)
Book
Robust statistical procedures
TL;DR: In this paper, the authors discuss the first ten years of the first decade of the 21st century and the role of robustness in the development of the Internet. But they do not discuss the future directions of robust procedures.
Journal ArticleDOI
Robust estimation: A condensed partial survey
TL;DR: In this paper, the authors present a survey of recent work in mathematical statistics and probability theory with a focus on the use of robust estimators, such as weak*-continuous functionals serving as robustified maximum likelihood estimators.