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High-breakdown robust multivariate methods (Q900488)

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Language	Label	Description	Also known as
English	High-breakdown robust multivariate methods	scientific article

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scholarly article

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High-breakdown robust multivariate methods (English)

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zbMATH Open document ID

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10.1214/088342307000000087

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Peter J. Rousseeuw

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Stefan Van Aelst

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Statistical Science

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publication date

22 December 2015

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full work available at URL

https://arxiv.org/abs/0808.0657

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https://projecteuclid.org/euclid.ss/1215441287

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Mathematics Subject Classification ID

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zbMATH DE Number

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zbMATH Keywords

breakdown value

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influence function

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multivariate statistics

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outliers

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partial least squares

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principal components

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regression

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robustness

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describes a project that uses

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MaRDI profile type

MaRDI publication profile

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Bias robustness of three median-based regression estimates.

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The multivariate least-trimmed squares estimator

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Robust Estimates of Location: Survey and Advances

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Asymptotic distributions of the maximal depth estimators for regression and multivariate location

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The Masking Breakdown Point of Multivariate Outlier Identification Rules

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Maximum bias curves for robust regression with non-elliptical regressors

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Influence functions and outlier detection under the common principal components model: A robust approach

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Some Theorems on Quadratic Forms Applied in the Study of Analysis of Variance Problems, I. Effect of Inequality of Variance in the One-Way Classification

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Asymptotics for the minimum covariance determinant estimator

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Robust Procedures in Multivariate Analysis I: Robust Covariance Estimation

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Robust Inference for Generalized Linear Models

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A Bounded Influence, High Breakdown, Efficient Regression Estimator

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High-Breakdown Inference for Mixed Linear Models

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Robust linear discriminant analysis using S-estimators

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Estimators of the multiple correlation coefficient: local robustness and confidence intervals

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Robust factor analysis.

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Influence function and efficiency of the minimum covariance determinant scatter matrix estimator

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Principal component analysis based on robust estimators of the covariance or correlation matrix: influence functions and efficiencies

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Generalized S-Estimators

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High breakdown estimators for principal components: the projection-pursuit approach revis\-ited

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Trimmed \(k\)-means: An attempt to robustify quantizers

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Asymptotic distributions of principal components based on robust dispersions

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Asymptotic behaviour of S-estimates of multivariate location parameters and dispersion matrices

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The asymptotics of Rousseeuw's minimum volume ellipsoid estimator

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An efficient Fréchet differentiable high breakdown multivariate location and dispersion estimator

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Breakdown and groups. (With discussions and rejoinder)

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Breakdown properties of location estimates based on halfspace depth and projected outlyingness

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A Class of Locally and Globally Robust Regression Estimates

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Outlier robust analysis of long-run marketing effects for weekly scanning data

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A Projection Pursuit Algorithm for Exploratory Data Analysis

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Robust estimation for the multivariate linear model based on a \(\tau\)-scale

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Outlier detection in the multiple cluster setting using the minimum covariance determinant estimator

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High-Breakdown Linear Discriminant Analysis

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Inconsistency of Resampling Algorithms for High-Breakdown Regression Estimators and a New Algorithm

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High breakdown estimation for multiple populations with applications to discriminant analysis

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Lower bounds for contamination bias: Globally minimax versus locally linear estimation

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Breakdown points of t-type regression estimators

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Rank-Based Estimates in the Linear Model with High Breakdown Point

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Robust regression: Asymptotics, conjectures and Monte Carlo

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Robust Statistics

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Projection pursuit

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Robust regression with both continuous and binary regressors

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Fast and robust discriminant analysis

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Nonparametric Estimate of Regression Coefficients

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Finding Groups in Data

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Constrained \(M\)-estimation for multivariate location and scatter

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L-Estimation for Linear Models

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Efficient Bounded-Influence Regression Estimation

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Conditionally Unbiased Bounded-Influence Estimation in General Regression Models, with Applications to Generalized Linear Models

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Projection-Pursuit Approach to Robust Dispersion Matrices and Principal Components: Primary Theory and Monte Carlo

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Multivariate analysis by data depth: Descriptive statistics, graphics and inference. (With discussions and rejoinder)

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Robust principal component analysis for functional data. (With comments)

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On the relation between S-estimators and M-estimators of multivariate location and covariance

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Multivariate τ-Estimators for Location and Scatter

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Asymptotics of reweighted estimators of multivariate location and scatter

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Breakdown points of affine equivariant estimators of multivariate location and covariance matrices

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Weighted Likelihood Equations with Bootstrap Root Search

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Bounded Influence and High Breakdown Point Testing Procedures in Linear Models

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Robust Bounded-Influence Tests in Linear Models

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Robust m-estimators of multivariate location and scatter

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Robust Statistics

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Bias-robust estimators of multivariate scatter based on projections

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Asymptotic behavior of general M-estimates for regression and scale with random carriers

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Bias-robust estimates of regression based on projections

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The Behavior of the Stahel-Donoho Robust Multivariate Estimator

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Robust regression with both continuous and categorical predictors

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Influence functionals for time series (with discussion)

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Min-max bias robust regression

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On depth and deep points: A calculus.

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Robust estimates for arch processes

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Breakdown points of trimmed likelihood estimators and related estimators in generalized linear models.

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Outlier Robust Model Selection in Linear Regression

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Small sample corrections for LTS and MCD

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Robustness properties of \(S\)-estimators of multivariate location and shape in high dimension

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Identification of Outliers in Multivariate Data

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Robust Linear Model Selection by Cross-Validation

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A Robust Version of Mallows's C p

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Least Median of Squares Regression

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Robustness against separation and outliers in logistic regression

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Alternatives to the Median Absolute Deviation

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Regression Depth

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Principal Components Analysis Based on Multivariate MM Estimators With Fast and Robust Bootstrap

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Bootstrapping robust estimates of regression

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Robust regression using repeated medians

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On One-Step GM Estimates and Stability of Inferences in Linear Regression

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Functional stability of one-step GM-estimators in approximately linear regression

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Computation of High Breakdown Nonlinear Regression Parameters

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Breakdown in Nonlinear Regression

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On the uniqueness of \(S\)-functionals and \(M\)-functionals under nonelliptical distributions.

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Finite sample breakdown points of projection based multivariate location and scatter statistics

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Robustness of deepest regression

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The deepest regression method

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A robust Hotelling test

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Computable Robust Estimation of Multivariate Location and Shape in High Dimension Using Compound Estimators

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High breakdown-point and high efficiency robust estimates for regression

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High Breakdown-Point Estimates of Regression by Means of the Minimization of an Efficient Scale

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Robust estimation in the errors-in-variables model

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Bias robust estimation in orthogonal regression

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On the Stahel-Donoho estimator and depth-weighted means of multivariate data.

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General notions of statistical depth function.

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Nonparametric notions of multivariate ''scatter measure'' and ''more scattered'' based on statistical depth functions

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Sitelinks

Mathematics(1 entry)

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