Robust statistics in data analysis — A review

Daszykowski, M.; Kaczmarek, Krzysztof; Heyden, Yvan Vander; Walczak, Beata

doi:10.1016/j.chemolab.2006.06.016

Cited by 297 publications

(143 citation statements)

References 43 publications

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“…Several ways of robustifying principal components have been proposed (Daszykowski et al, 2007;Filzmoser et al, 2008;Rousseeuw et al, 2006). To enable the comparison of different robust methods, measures of performance are necessary.…”

Section: Classical Robust Pca Methodsmentioning

confidence: 99%

“…After a brief state of the art on fault isolation, structured residuals are generated for multiple fault isolation. These structured residuals are based on the reconstruction principle of process variables (Dunia et al, 1996;Wang et al, 2004a;b). However, instead of considering all the subsets of faulty variables (one up to all sensors), we determine the isolable multiple fault by evaluating the existence condition of these structured residuals.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Sensor Fault Detection and Isolation by Robust Principal Component Analysis

Tharrault¹,

Harkat²,

Mourot³

et al. 2010

Fault Detection

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Section: Classical Robust Pca Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sensor Fault Detection and Isolation by Robust Principal Component Analysis

Tharrault¹,

Harkat²,

Mourot³

et al. 2010

Fault Detection

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“…It is well known that including outliers in model development has adverse impact on the prediction accuracy. Due to its importance, outlier detection has been extensively discussed in the literature; an overview of the current status and some recent development can be found in [55][56][57]. In this work, the built-in outlier detection capability of PLS [5] is utilized and no obvious outliers are found in the two datasets under investigation.…”

Section: Implemental Detailsmentioning

confidence: 99%

Bagging for robust non-linear multivariate calibration of spectroscopy

Wang

Chen

Lau

2011

Chemometrics and Intelligent Laboratory Systems

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“…Because individual data are replaced by quantiles of the data, this method is less sensitive to outliers. It is therefore a robust equivalent of MLE (daszykowksi, Kaczmarek, vander Heyden, & walczak, 2007). MPQ, however, is sensitive to non-regular distributions.…”

Section: Alternatives To Likelihoodmentioning

confidence: 99%

Likelihood and its use in Parameter Estimation and Model Comparison

Cousineau

Allan

2016

mee

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Parameter estimation and model fitting underlie many statistical procedures. Whether the objective is to examine central tendency or the slope of a regression line, an estimation method must be used. Likelihood is the basis for parameter estimation, for determining the best relative fit among several statistical models, and for significance testing. In this review, the concept of Likelihood is explained and applied computation examples are given. The examples provided serve to illustrate how likelihood is relevant, and related to, the most frequently applied test statistics (Student’s t-test, ANOVA). Additional examples illustrate the computation of Likelihood(s) using common population model assumptions (e.g., normality) and alternative assumptions for cases where data are non-normal. To further describe the interconnectedness of Likelihood and the Likelihood Ratio with modern test statistics, the relationship between Likelihood, Least Squares Modeling, and Bayesian Inference are discussed. Finally, the advantages and limitations of Likelihood methods are listed, alternatives to Likelihood are briefly reviewed, and R code to compute each of the examples in the text is provided.L’estimation de paramètres et l’ajustement de modèles est au coeur de toutes procédures statistiques. Que l’objectif soit d’examiner la tendance centrale ou une pente de régression, une méthode d’estimation est nécessaire. La fonction de vraisemblance est la pierre angulaire sur laquelle repose l’estimation de paramètres, les tests d’hypothèses et la comparaison de modèles. Cet article présente le concept de vraisemblance et les tests statistiques communément utilisés (tests t, ANOVA). Certains exemples présentent le calcul de la fonction de vraisemblance lorsque le postulat de normalité est présent et lorsqu’il n’est pas adéquat. Les liens entre vraisemblance, rapport de vraisemblance, méthodes des moindres carrés et bayésienne sont discutés. Finalement, les forces et les faiblesses des méthodes basées sur la vraisemblance sont énumérées et des méthodes alternatives sont mentionnées. Des instructions en R sont données pour tester les exemples du texte.A estimativa de parâmetros e o ajustamento de modelos está no cerne de todos os procedimentos estatísticos. Se o objetivo é analisar a tendência central ou uma inclinação de regressão, é necessário um método de estimativa. A função de verossimilhança é a pedra angular sobre a qual assentam a estimativa de parâmetros, os testes de hipóteses e a comparação de modelos. Este artigo introduz o conceito de verosimilhança e os testes estatísticos vulgarmente utilizados (testes t, ANOVA). Alguns exemplos mostram o cálculo da função de verossimilhança quando o pressuposto de normalidade está presente e sempre que não é adequado. Discutem-se as ligações entre a verosimilhança, razão de verossimilhança, os métodos dos mínimos quadrados e o bayesianismo. Por fim, são enumeradas as forças e as fraquezas dos métodos baseados na verosimilhança e são mencionados os métodos alternativos. As instruções em R s...

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Robust statistics in data analysis — A review

Cited by 297 publications

References 43 publications

Sensor Fault Detection and Isolation by Robust Principal Component Analysis

Sensor Fault Detection and Isolation by Robust Principal Component Analysis

Bagging for robust non-linear multivariate calibration of spectroscopy

Likelihood and its use in Parameter Estimation and Model Comparison

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