Influence function and maximum bias of projection depth based estimators.

DOI10.1214/aos/1079120133zbMath1105.62350OpenAlexW2040527709MaRDI QIDQ1884610

Yanyan Li

Publication date: 5 November 2004

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.aos/1079120133

zbMATH Keywords

robustnessinfluence functionbreakdown pointweighted meanprojection depthprojection mediangross error sensitivitycontamination sensitivitymaxiumum bias

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Estimation in multivariate analysis (62H12) Characterization and structure theory for multivariate probability distributions; copulas (62H05) Robustness and adaptive procedures (parametric inference) (62F35)

Related Items

EXPECTED MAXIMIZATION ALGORITHM: PROJECTION DEPTH APPROACH ⋮ Exactly computing bivariate projection depth contours and median ⋮ Robust mean-variance portfolio through the weighted \(L^p\) depth function ⋮ Robust estimating equation based on statistical depth ⋮ Multidimensional trimming based on projection depth ⋮ Robustness and asymptotics of the projection median ⋮ Some results on the computing of Tukey's halfspace median ⋮ On the use of \(L\)-functionals in regression models ⋮ Central limit theorem and influence function for the MCD estimators at general multivariate distributions ⋮ High dimensional data analysis using multivariate generalized spatial quantiles ⋮ Unnamed Item ⋮ On the behavior of Tukey's depth and median under symmetric stable distributions. ⋮ Generalized and robustified empirical depths for multivariate data ⋮ Multivariate trimmed means based on the Tukey depth ⋮ A new projection estimate for multivariate location with minimax bias ⋮ Depth weighted scatter estimators ⋮ Influence functions of some depth functions, and application to depth-weighted L-statistics ⋮ Robust Estimation of Multivariate Linear Model Based on Depth Weighted Mean and Scatter ⋮ Robustness of the deepest projection regression functional

Cites Work

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• Min-max bias robust regression
• On a notion of data depth based on random simplices
• On the projections of isotropic distributions
• Breakdown properties of location estimates based on halfspace depth and projected outlyingness
• Finite sample breakdown points of projection based multivariate location and scatter statistics
• Projection-based depth functions and associated medians
• Multivariate analysis by data depth: Descriptive statistics, graphics and inference. (With discussions and rejoinder)
• General notions of statistical depth function.
• The influence function and maximum bias of Tukey's median
• Projection estimates of multivariate location
• On the Stahel-Donoho estimator and depth-weighted means of multivariate data.
• On the performance of some robust nonparametric location measures relative to a general notion of multivariate symmetry
• Lower bounds for contamination bias: Globally minimax versus locally linear estimation
• The Behavior of the Stahel-Donoho Robust Multivariate Estimator
• Robust Estimation of a Location Parameter
• Influence function of halfspace depth

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