Bias-robust estimators of multivariate scatter based on projections

DOI10.1016/0047-259X(92)90084-SzbMath0777.62057OpenAlexW2050254378MaRDI QIDQ1261307

Werner A. Stahel, Ricardo Antonio Maronna, Víctor J. Yohai

Publication date: 1 September 1993

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0047-259x(92)90084-s

zbMATH Keywords

algorithmasymptoticscovariance matrixspherical symmetrybiashigh breakdown point estimationcondition numberssphericaltransformation matrixequivariant estimationscatter matrixminimum volume ellipsoid estimatormedian absolute deviationbias-robust estimatorsnew class of projection estimatorsrobust scale functionalsimulations of finite samplesspread of univariate projections

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Robustness and adaptive procedures (parametric inference) (62F35)

Related Items

Combining locally and globally robust estimates for regression, Projection estimates of multivariate location, Local and global robustness of regression estimators, Robust estimation in simultaneous equations models, An easy way to increase the finite-sample efficiency of the resampled minimum volume ellipsoid estimator, High-breakdown robust multivariate methods, Robust weighted orthogonal regression in the errors-in-variables model, The finite sample breakdown point of PCS, Some extensions of Tukey's depth function, Invariant Co-Ordinate Selection, Highly robust estimation of dispersion matrices, A note on multivariate location and scatter statistics for sparse data sets, Functional stability of one-step GM-estimators in approximately linear regression, On the Breakdown Properties of Some Multivariate M-Functionals*, Projection based scatter depth functions and associated scatter estimators, Some results for robust GM-based estimators in heteroscedastic regression models

Uses Software

• robustbase

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Algorithms for the computation of weights in bounded influence regression
• On the relation between S-estimators and M-estimators of multivariate location and covariance
• A distribution-free M-estimator of multivariate scatter
• Asymptotic behaviour of S-estimates of multivariate location parameters and dispersion matrices
• Robust m-estimators of multivariate location and scatter
• Projection-Pursuit Approach to Robust Dispersion Matrices and Principal Components: Primary Theory and Monte Carlo
• Some Results on the Existence, Uniqueness, and Computation of the M-Estimates of Multivariate Location and Scatter
• Robust Estimation of Dispersion Matrices and Principal Components
• The maximum bias of robust covariances
• Robust Statistics
• Sparse components of images and optimal atomic decompositions