The multivariate least-trimmed squares estimator

Agulló, José Julio Espina; Croux, Christophe; Aelst, Stefan Van

doi:10.1016/j.jmva.2006.06.005

Cited by 113 publications

(90 citation statements)

References 24 publications

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“…To avoid this problem we propose a robust Cronbach's alpha estimate that is able to resist outliers and thus measures the internal consistency of the most central part of the observations. A robust measure of reliability was already proposed by Wilcox [34] who used the midvariance and midcovariance as robust estimates for the variances and covariances in (1). In this paper we propose to estimate the covariance matrix of (Y 1 , .…”

Section: Introductionmentioning

confidence: 99%

“…. , Y p ) t using a robust estimator and then we substitute the elements of this robust covariance estimate in (1).…”

Section: Introductionmentioning

confidence: 99%

“…Recently, robust multivariate statistical methods based on robust estimation of location and scatter have been developed and investigated such as factor analysis [20], principal component analysis [7,30], canonical correlation analysis [5,31] and multivariate regression [26,33,1]. See also [21] for an overview.…”

Section: Introductionmentioning

confidence: 99%

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Robust estimation of Cronbach's alpha

Christmann

Aelst

2006

Journal of Multivariate Analysis

266

125

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Cronbach's alpha is a popular method to measure reliability, e.g. in quantifying the reliability of a score to summarize the information of several items in questionnaires. The alpha coefficient is known to be non-robust. We study the behavior of this coefficient in different settings to identify situations where Cronbach's alpha is extremely sensitive to violations of the classical model assumptions. Furthermore, we construct a robust version of Cronbach's alpha which is insensitive to a small proportion of data that belong to a different source. The idea is that the robust Cronbach's alpha reflects the reliability of the bulk of the data. For example, it should not be possible that some small amount of outliers makes a score look reliable if it is not.

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Section: Introductionmentioning

confidence: 99%

“…. , Y p ) t using a robust estimator and then we substitute the elements of this robust covariance estimate in (1).…”

Section: Introductionmentioning

confidence: 99%

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Robust estimation of Cronbach's alpha

Christmann

Aelst

2006

Journal of Multivariate Analysis

266

125

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“…We will use the Multivariate Least Trimmed Squares estimator, introduced by Agull6, Croux and Van Aelst (2002). This estimator is defined by minimizing a trimmed sum of a squared Mahalanobis distances, and can be computed by a fast algorithm.…”

Section: Introductionmentioning

confidence: 99%

Robust Estimation of the Vector Autoregressive Model by a Least Trimmed Squares Procedure

Croux

Joossens

Compstat 2008

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The vector autoregressive model is very popular for modeling multiple time series.Estimation of its parameters is done by a least squares procedure. However, this estimation method is unreliable when outliers are present in the data, and there is a need for robust alternatives. In this paper we propose to estimate the vector autoregressive model by using a trimmed least squares estimator. We show how the order of the autoregressive model can be determined in a robust way, and how confidence bounds around the robustly estimated impulse response functions can be constructed. The resistance of the estimators to outliers is studied on real and simulated data.

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“…Robust regression approaches are usually used to remove influence of outliers [11][12][13]. Several well-known examples include M-estimators [14], least median of squares (LMS) [15], least trimmed squares (LTS) [16], robust principal component regression (RPCR) [17], robust partial least squares (RPLS) [18,19] and robust principal components regression based on principal sensitivity vectors (RPPSV) [20]. The resultant regression models optimally account for the bulk of data points.…”

Section: Introductionmentioning

confidence: 99%

Toward better QSAR/QSPR modeling: simultaneous outlier detection and variable selection using distribution of model features

Cao

Liang

et al. 2010

J Comput Aided Mol Des

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Building a robust and reliable QSAR/QSPR model should greatly consider two aspects: selecting the optimal variable subset from a large pool of molecular descriptors and detecting outliers from a pool of samples. The two problems have the specific similarity and complementarity to some extent. Given a particular learning algorithm on a particular data set, one should consider how the interaction could happen between variable selection and outlier detection. In this paper, we describe a consistent methodology for simultaneously performing variable subset selection and outlier detection using the idea of statistical distribution which can be simulated by the establishment of many cross-predictive linear models. The approach exploits the fact that the distribution of linear model coefficients provides a mechanism for ranking and interpreting the effects of variable, while the distribution of prediction errors provides a mechanism for differentiating the outliers from normal samples. The use of statistic of these distributions, namely mean value and standard deviation, inherently provides a feasible way to effectively describe the information contained by the original samples. Several examples are used to demonstrate the prediction ability of our proposed approach through the comparison of different approaches as well as their combinations.

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The multivariate least-trimmed squares estimator

Cited by 113 publications

References 24 publications

Robust estimation of Cronbach's alpha

Robust estimation of Cronbach's alpha

Robust Estimation of the Vector Autoregressive Model by a Least Trimmed Squares Procedure

Toward better QSAR/QSPR modeling: simultaneous outlier detection and variable selection using distribution of model features

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