Robust Estimates of Location and Dispersion for High-Dimensional Datasets

Maronna, Ricardo A.; Zamar, Ruben H.

doi:10.1198/004017002188618509

Cited by 348 publications

(280 citation statements)

References 22 publications

Supporting

Mentioning

273

Contrasting

Unclassified

Order By: Relevance

“…To avoid a masking effect caused by (multivariate) outliers, a robust estimator should be used. Lanius and Gather suggest the fast computable orthogonalized Gnanadesikan-Kettenring estimator (OGK) by Maronna and Zamar (2002). The maximum possible explosion breakdown point of the OGK is equal to that of a univariate estimator of scale the OGK depends on.…”

Section: The Online Trimmed Repeated Median-least Squares (Otrm-ls) Fmentioning

confidence: 99%

See 1 more Smart Citation

Multivariate Real-Time Signal Extraction by a Robust Adaptive Regression Filter

Borowski

Schettlinger

Gather

2009

Communications in Statistics - Simulation and Computation

View full text Add to dashboard Cite

Section: The Online Trimmed Repeated Median-least Squares (Otrm-ls) Fmentioning

confidence: 99%

“…We follow a proposal by Maronna and Zamar (2002), where d 0 is adapted via the median of the distances d (1), . .…”

Section: The Online Trimmed Repeated Median-least Squares (Otrm-ls) Fmentioning

confidence: 99%

Multivariate Real-Time Signal Extraction by a Robust Adaptive Regression Filter

Borowski

Schettlinger

Gather

2009

Communications in Statistics - Simulation and Computation

View full text Add to dashboard Cite

“…So computational details related to these other estimators are not provided. They included the minimum volume ellipsoid (MVE) estimator (Rousseeuw & van Zomeren, 1990), the minimum covariance determinant (MCD) estimator (Rousseeuw & Van Driessen, 1999), the translated-biweight S-estimator (Rocke, 1996), the median ball algorithm (Olive, 2004) and the orthogonal Gnanadesikan-Kettenring (OGK) estimator (Maronna & Zamar, 2002).…”

Section: The Location Estimatorsmentioning

confidence: 99%

Within Groups ANOVA When Using a Robust Multivariate Measure of Location

Wilcox¹,

Hayes²

2016

J. Mod. App. Stat. Meth.

View full text Add to dashboard Cite

For robust measures of location associated with J dependent groups, various methods have been proposed that are aimed at testing the global hypothesis of a common measure of location applied to the marginal distributions. A criticism of these methods is that they do not deal with outliers in a manner that takes into account the overall structure of the data. Location estimators have been derived that deal with outliers in this manner, but evidently there are no simulation results regarding how well they perform when the goal is to test the some global hypothesis. The paper compares four bootstrap methods in terms of their ability to control the Type I error probability when the sample size is small, two of which were found to perform poorly. The choice of location estimator was found to be important as well. Indeed, for several of the estimators considered here, control over the Type I error probability was very poor. Only one estimator performed well when using the first of two general approaches that might be used. It is based on a variation of the (affine equivariant) Donoho-Gasko trimmed mean. For the second general approach, only a skipped estimator performed reasonably well. (It removes outliers via a projection method and averages the remaining data.) Only one bootstrap method was found to perform well when using the first approach. A different bootstrap method is recommended when using the second approach.

show abstract

“…• Three pairs of location and scatter estimators: classical (x, S) with asymptotic detection limits; RMCD25 [11] and OGK (2) (0.9) [9] with detection limits determined previously by simulation with 10000 normal data sets.…”

Section: Simulation Studymentioning

confidence: 99%

Robust Clustering Method for the Detection of Outliers: Using AIC to Select the Number of Clusters

Santos-Pereira

Pires

2013

Studies in Theoretical and Applied Statistics

View full text Add to dashboard Cite

In [14] we proposed a method to detect outliers in multivariate data based on clustering and robust estimators. To implement this method in practice it is necessary to choose a clustering method, a pair of location and scatter estimators, and the number of clusters, k. After several simulation experiments it was possible to give a number of guidelines regarding the first two choices. However the choice of the number of clusters depends entirely on the structure of the particular data set under study. Our suggestion is to try several values of k (e.g. from 1 to a maximum reasonable k which depends on the number of observations and on the number of variables) and select k minimizing an adapted AIC. In this paper we analyze this AIC based criterion for choosing the number of clusters k (and also the clustering method and the location and scatter estimators) by applying it to several simulated data sets with and without outliers.

show abstract

Robust Estimates of Location and Dispersion for High-Dimensional Datasets

Cited by 348 publications

References 22 publications

Multivariate Real-Time Signal Extraction by a Robust Adaptive Regression Filter

Multivariate Real-Time Signal Extraction by a Robust Adaptive Regression Filter

Within Groups ANOVA When Using a Robust Multivariate Measure of Location

Robust Clustering Method for the Detection of Outliers: Using AIC to Select the Number of Clusters

Contact Info

Product

Resources

About