Multivariate Outlier Detection With High-Breakdown Estimators

Cerioli, Andrea

doi:10.1198/jasa.2009.tm09147

Cited by 121 publications

(96 citation statements)

References 22 publications

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“…[12,5]). However the performance of that procedure is still highly dependent of multivariate normality of the bulk of the data [2], or on the data being elliptically contoured. To avoid this dependency, a method to detect outliers in multivariate data based on clustering and robust estimators was introduced in [14].…”

Section: Methodsmentioning

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

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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.

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Section: Methodsmentioning

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

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“…If alphaX is in the interval (0.5, 1), adaptive TCLUST-REG is used and this parameter indicates a Bonferronized confidence level to be used to identify the units subject to second level trimming. If p > 1, the default estimator which is used is the forward search, on the other hand, if p = 1 we use a reweighted MCD as modified by Cerioli (2010). Finally, if alphaX is equal to 1, TCWRM is used and the user can supply the value of c X as the second element of the other input parameter restrfact.…”

Section: Lack Of Robustness and An Adaptive Trimming Proposalmentioning

confidence: 99%

“…This means that the robust distances are compared with the confidence bands at a selected confidence level, and the observations with distances exceeding the bands are trimmed. In this case the multivariate outlier detection procedure proposed by Cerioli (2010), based on the reweighted MCD estimator (Rousseeuw and Van Driessen 1999), or the Forward Search (Riani et al 2009) can be used at each concentration step of each starting subset. The observations surviving to the two trimming steps are then used for updating the regression coefficients, weights and scatter matrices.…”

Section: Lack Of Robustness and An Adaptive Trimming Proposalmentioning

confidence: 99%

“…5 Boxplots of the classification errors (left panels) and group-wise slope biases (right panels) obtained in the 1000 data configurations corresponding to lines 5 (top panels) and 6 (bottom panels) of Table 1 calculated at a confidence level specified by the user. The identification of the units is done using either the Finite Sample Re-weighted MCD rule (Cerioli 2010) or the Forward Search (Riani et al 2009) for their good trade-off between robustness and efficiency. TCLUST (García-Escudero et al 2008), which in the univariate case is equivalent to the MCD, can be also used.…”

Section: Adaptive Tclust-reg Vs Tcwrmmentioning

confidence: 99%

“…To address the problem we have introduced a new methodological option in TCLUST-REG, through the possibility to regulate the percentage of second level trimming during the estimation steps. This is done through an adaptive approach based either on the Forward Search (Riani et al 2009), or on the Finite Sample Re-weighted MCD method of Cerioli (2010).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Assessing trimming methodologies for clustering linear regression data

Torti

Perrotta

Riani

et al. 2018

Adv Data Anal Classif

Self Cite

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We assess the performance of state-of-the-art robust clustering tools for regression structures under a variety of different data configurations. We focus on two methodologies that use trimming and restrictions on group scatters as their main ingredients. We also give particular care to the data generation process through the development of a flexible simulation tool for mixtures of regressions, where the user can control the degree of overlap between the groups. Level of trimming and restriction factors are input parameters for which appropriate tuning is required. Since we find that incorrect specification of the second-level trimming in the Trimmed CLUSTering REGression model (TCLUST-REG) can deteriorate the performance of the method, we propose an improvement where the second-level trimming is not fixed in advance but is data dependent. We then compare our adaptive version of TCLUST-REG with the Trimmed Cluster Weighted Restricted Model (TCWRM) which provides a powerful extension of the robust clusterwise regression methodology. Our overall conclusion is that the two methods perform comparably, but with notable differences due to the inherent degree of modeling implied by them.

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Outliers

Aelst¹

2012

Encyclopedia of Environmetrics

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Datasets frequently contain outliers which are observations that strongly deviate from the pattern in the majority of the data. Detecting outliers and measuring their influence on an estimation procedure is not trivial. In one or two dimensions graphical inspection of the data may be helpful, but in higher dimensions more reliable methods are needed. We discuss robust estimation to obtain estimates that can resist the influence of outliers and related outlier diagnostics to identify the outliers in a dataset.

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Multivariate Outlier Detection With High-Breakdown Estimators

Cited by 121 publications

References 22 publications

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

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

Assessing trimming methodologies for clustering linear regression data

Outliers

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