On the Breakdown Properties of Some Multivariate M-Functionals*

DOI10.1111/j.1467-9469.2005.00425.xzbMath1089.62056OpenAlexW1998416944MaRDI QIDQ5467691

David E. Tyler, Lutz Dümbgen

Publication date: 24 May 2006

Published in: Scandinavian Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1111/j.1467-9469.2005.00425.x

zbMATH Keywords

M-estimatescatter matrixcoplanar contaminationelliptical t-distributiontight contamination

Mathematics Subject Classification ID

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

Related Items (24)

Influence Functions and Efficiencies of k-Step Hettmansperger–Randles Estimators for Multivariate Location and Regression ⋮ AFFINE-EQUIVARIANT SPATIAL MEDIAN AND ITS USE IN THE MULTIVARIATE MULTI-SAMPLE LOCATION PROBLEM ⋮ Computationally easy outlier detection via projection pursuit with finitely many directions ⋮ Robust factored principal component analysis for matrix-valued outlier accommodation and detection ⋮ Multivariate Myriad Filters Based on Parameter Estimation of Student-$t$ Distributions ⋮ Robust subspace recovery by Tyler's M-estimator ⋮ Robustifying principal component analysis with spatial sign vectors ⋮ The \(k\)-step spatial sign covariance matrix ⋮ Optimal rank-based tests for homogeneity of scatter ⋮ Symmetrised M-estimators of multivariate scatter ⋮ A generalization of Tyler's M-estimators to the case of incomplete data ⋮ Inference on the shape of elliptical distributions based on the MCD ⋮ \(k\)-step shape estimators based on spatial signs and ranks ⋮ Tests and estimates of shape based on spatial signs and ranks ⋮ A canonical definition of shape ⋮ Equivariance and invariance properties of multivariate quantile and related functions, and the role of standardisation ⋮ Optimal tests for homogeneity of covariance, scale, and shape ⋮ Multivariate generalized S-estimators ⋮ Differentiability of \(t\)-functionals of location and scatter ⋮ Asymptotic distributions of robust shape matrices and scales ⋮ On jackknifing the symmetrized Tyler matrix ⋮ Unnamed Item ⋮ \(M\)-functionals of multivariate scatter ⋮ Robustness of the Affine Equivariant Scatter Estimator Based on the Spatial Rank Covariance Matrix

Cites Work

• Unnamed Item
• Bias-robust estimators of multivariate scatter based on projections
• On Tyler's \(M\)-functional of scatter in high dimension
• Minimax bias-robust estimation of the dispersion matrix of a multivariate distribution
• Constrained \(M\)-estimation for multivariate location and scatter
• On the uniqueness of \(S\)-functionals and \(M\)-functionals under nonelliptical distributions.
• Optimal tests for multivariate location based on interdirections and pseudo-Mahalanobis ranks.
• A practical affine equivariant multivariate median
• Robust Statistics

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