Minimum covariance determinant and extensions

M Hubert, M Debruyne… - Wiley Interdisciplinary …, 2018 - Wiley Online Library
The minimum covariance determinant (MCD) method is a highly robust estimator of
multivariate location and scatter, for which a fast algorithm is available. Since estimating the …

Minimum covariance determinant

M Hubert, M Debruyne - Wiley interdisciplinary reviews …, 2010 - Wiley Online Library
The minimum covariance determinant (MCD) estimator is a highly robust estimator of
multivariate location and scatter. It can be computed efficiently with the FAST‐MCD …

Robust estimation of Cronbach's alpha

A Christmann, S Van Aelst - Journal of Multivariate Analysis, 2006 - Elsevier
Cronbach's alpha is a popular method to measure reliability, eg in quantifying the reliability
of a score to summarize the information of several items in questionnaires. The alpha …

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

C Croux, G Haesbroeck - Biometrika, 2000 - academic.oup.com
A robust principal component analysis can be easily performed by computing the
eigenvalues and eigenvectors of a robust estimator of the covariance or correlation matrix. In …

High-breakdown robust multivariate methods

M Hubert, PJ Rousseeuw, S Van Aelst - 2008 - projecteuclid.org
When applying a statistical method in practice it often occurs that some observations deviate
from the usual assumptions. However, many classical methods are sensitive to outliers. The …

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

C Croux, G Haesbroeck - Journal of Multivariate Analysis, 1999 - Elsevier
The minimum covariance determinant (MCD) scatter estimator is a highly robust estimator
for the dispersion matrix of a multivariate, elliptically symmetric distribution. It is relatively fast …

Minimum volume ellipsoid

S Van Aelst, P Rousseeuw - Wiley Interdisciplinary Reviews …, 2009 - Wiley Online Library
The minimum volume ellipsoid (MVE) estimator is based on the smallest volume ellipsoid
that covers h of the n observations. It is an affine equivariant, high‐breakdown robust …

Finding an unknown number of multivariate outliers

M Riani, AC Atkinson, A Cerioli - Journal of the Royal Statistical …, 2009 - academic.oup.com
We use the forward search to provide robust Mahalanobis distances to detect the presence
of outliers in a sample of multivariate normal data. Theoretical results on order statistics and …

Invariant co-ordinate selection

DE Tyler, F Critchley, L Dümbgen… - Journal of the Royal …, 2009 - academic.oup.com
A general method for exploring multivariate data by comparing different estimates of
multivariate scatter is presented. The method is based on the eigenvalue–eigenvector …

Robust multivariate regression

PJ Rousseeuw, S Van Aelst, K Van Driessen… - Technometrics, 2004 - Taylor & Francis
We introduce a robust method for multivariate regression based on robust estimation of the
joint location and scatter matrix of the explanatory and response variables. As a robust …