Central limit theorem and influence function for the MCD estimators at general multivariate distributions

DOI10.3150/11-BEJ353zbMath1239.62068arXiv0907.0079MaRDI QIDQ418235

Eric A. Cator, Hendrik P. Lopuhaä

Publication date: 28 May 2012

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0907.0079

zbMATH Keywords

asymptotic normalityinfluence functionminimum covariance determinant

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Asymptotic properties of parametric estimators (62F12) Estimation in multivariate analysis (62H12) Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05) Characterization and structure theory for multivariate probability distributions; copulas (62H05)

Related Items (16)

Robust multiple-set linear canonical analysis based on minimum covariance determinant estimator ⋮ A robust deterministic affine-equivariant algorithm for multivariate location and scatter ⋮ Robust estimation of precision matrices under cellwise contamination ⋮ Common multivariate estimators of location and scatter capture the symmetry of the underlying distribution ⋮ Multivariate Hill Estimators ⋮ Consistency factor for the MCD estimator at the Student-\(t\) distribution ⋮ On Huber's contaminated model ⋮ A further study comparing forward search multivariate outlier methods including ATLA with an application to clustering ⋮ Efficient inference about the tail weight in multivariate Student \(t\) distributions ⋮ On robust classification using projection depth ⋮ Wild adaptive trimming for robust estimation and cluster analysis ⋮ The minimum regularized covariance determinant estimator ⋮ Inference on the shape of elliptical distributions based on the MCD ⋮ ICS for Multivariate Outlier Detection with Application to Quality Control ⋮ A two-stage Bayesian semiparametric model for novelty detection with robust prior information ⋮ Outlier detection via a block diagonal product estimator

Uses Software

• FastICA

Cites Work

• Unnamed Item
• Unnamed Item
• Invariant Co-Ordinate Selection
• Asymptotic expansion of the minimum covariance determinant estimators
• Breakdown points of affine equivariant estimators of multivariate location and covariance matrices
• High-breakdown robust multivariate methods
• Robust dimension reduction based on canonical correlation
• Principal component analysis for data containing outliers and missing elements
• Best approximations to random variables based on trimming procedures
• Asymptotics for the minimum covariance determinant estimator
• Trimmed \(k\)-means: An attempt to robustify quantizers
• Robust weighted orthogonal regression in the errors-in-variables model
• A central limit theorem for multivariate generalized trimmed \(k\)-means
• Depth weighted scatter estimators
• On the uniqueness of \(S\)-functionals and \(M\)-functionals under nonelliptical distributions.
• Robust factor analysis.
• On the Stahel-Donoho estimator and depth-weighted means of multivariate data.
• Influence function and maximum bias of projection depth based estimators.
• Influence function and efficiency of the minimum covariance determinant scatter matrix estimator
• The multivariate least-trimmed squares estimator
• Influence functions and efficiencies of the canonical correlation and vector estimates based on scatter and shape matrices
• Asymptotic expansion of S‐estimators of location and covariance
• High-Breakdown Linear Discriminant Analysis
• Principal component analysis based on robust estimators of the covariance or correlation matrix: influence functions and efficiencies
• Relations between Weak and Uniform Convergence of Measures with Applications
• Convergence of stochastic processes

This page was built for publication: Central limit theorem and influence function for the MCD estimators at general multivariate distributions