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Open AccessArticle

Multiple Outlier Detection Tests for Parametric Models

1
Institute of Applied Mathematics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania
2
Institute of Computer Science, Vilnius University, Didlaukio 47, LT-08303 Vilnius, Lithuania
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(12), 2156; https://doi.org/10.3390/math8122156
Received: 8 November 2020 / Revised: 27 November 2020 / Accepted: 30 November 2020 / Published: 3 December 2020
(This article belongs to the Section Probability and Statistics Theory)
We propose a simple multiple outlier identification method for parametric location-scale and shape-scale models when the number of possible outliers is not specified. The method is based on a result giving asymptotic properties of extreme z-scores. Robust estimators of model parameters are used defining z-scores. An extensive simulation study was done for comparing of the proposed method with existing methods. For the normal family, the method is compared with the well known Davies-Gather, Rosner’s, Hawking’s and Bolshev’s multiple outlier identification methods. The choice of an upper limit for the number of possible outliers in case of Rosner’s test application is discussed. For other families, the proposed method is compared with a method generalizing Gather-Davies method. In most situations, the new method has the highest outlier identification power in terms of masking and swamping values. We also created R package outliersTests for proposed test. View Full-Text
Keywords: location-scale models; outliers identification; unknown number of outliers; outlier region; robust estimators location-scale models; outliers identification; unknown number of outliers; outlier region; robust estimators
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MDPI and ACS Style

Bagdonavičius, V.; Petkevičius, L. Multiple Outlier Detection Tests for Parametric Models. Mathematics 2020, 8, 2156. https://doi.org/10.3390/math8122156

AMA Style

Bagdonavičius V, Petkevičius L. Multiple Outlier Detection Tests for Parametric Models. Mathematics. 2020; 8(12):2156. https://doi.org/10.3390/math8122156

Chicago/Turabian Style

Bagdonavičius, Vilijandas; Petkevičius, Linas. 2020. "Multiple Outlier Detection Tests for Parametric Models" Mathematics 8, no. 12: 2156. https://doi.org/10.3390/math8122156

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