The power of monitoring: how to make the most of a contaminated multivariate sample

Cerioli, Andrea; Riani, Marco; Atkinson, Anthony C.; Corbellini, Aldo

doi:10.1007/s10260-017-0409-8

Cited by 41 publications

(37 citation statements)

References 48 publications

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“…The results seem rarely sensitive to the choice of the tuning constants, which in our FSDA implementation are chosen to cover the most typical scenarios. Frameworks for monitoring the effects of parameters and tuning constants have been discussed in clustering by Cerioli et al (2017) and some discussants (García-Escudero et al 2017b;Farcomeni and Dotto 2018;Perrotta and Torti 2018).…”

Section: Choice Of Function Parameters and Tuning Constantsmentioning

confidence: 99%

Assessing trimming methodologies for clustering linear regression data

Torti

Perrotta

Riani

et al. 2018

Adv Data Anal Classif

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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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Section: Choice Of Function Parameters and Tuning Constantsmentioning

confidence: 99%

Assessing trimming methodologies for clustering linear regression data

Torti

Perrotta

Riani

et al. 2018

Adv Data Anal Classif

Self Cite

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show abstract

“…Copt and Victoria-Feser (2006) exploited this equivalence and proposed S-estimators in the balanced case, i.e. all clusters have the same dimension p. The difference with the multivariate model considered by Cerioli et al (2018) is that (i) μ i , the mean of the outcome y i for cluster i can be written as a linear combination of covariates, i.e. μ i = x T i α; (ii) , the variance of y i also have a specific structure, i.e.…”

Section: Mixed Linear Modelsmentioning

confidence: 99%

“…Geneva School of Economics and Management, Geneva University, Geneva, Switzerland in detecting the proportion of data that can be considered as outliers, hence providing information about the breakdown point for possible parameters tuning. Cerioli et al (2018) also compare several robust estimators, which incidentally, do not lead to the same breakdown point estimation.…”

Section: Introductionmentioning

confidence: 99%

“…As Cerioli et al (2018), we also consider estimation of a covariance matrix as a first step towards a more thorough data analysis. In what follows, we briefly mention robust methods that have been developed in multivariate settings, most of them under the multivariate normality assumption, for which the robust monitoring approach of Cerioli et al (2018) could possibly be extended.…”

Section: Introductionmentioning

confidence: 99%

“…In what follows, we briefly mention robust methods that have been developed in multivariate settings, most of them under the multivariate normality assumption, for which the robust monitoring approach of Cerioli et al (2018) could possibly be extended. We also discuss the important issue of robust inference (testing) and out-of-sample validity.…”

Section: Introductionmentioning

confidence: 99%

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Discussion of “The power of monitoring: how to make the most of a contaminated multivariate sample” by Andrea Cerioli, Marco Riani, Anthony C. Atkinson and Aldo Corbellini

Héritier

Victoria‐Feser

2017

Stat Methods Appl

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This paper discusses the contribution of Cerioli et al. (Stat Methods Appl, 2018), where robust monitoring based on high breakdown point estimators is proposed for multivariate data. The results follow years of development in robust diagnostic techniques. We discuss the issues of extending data monitoring to other models with complex structure, e.g. factor analysis, mixed linear models for which S and M Mestimators exist or deviating data cells. We emphasise the importance of robust testing that is often overlooked despite robust tests being readily available once S and M Mestimators have been defined. We mention open questions like out-of-sample inference or big data issues that would benefit from monitoring.

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