Geodesic
On outlier detection with the chebyshev type inequalities
Journal of the Belarusian State University. Mathematics and Informatics, Tome 3 (2020), pp. 28-35.

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This work considers algorithms of outlier detection based on the Chebyshev inequality. It compares these algorithms with such classical methods as Tukey’s boxplot, the $N$-sigma rule and its robust modifications based on $MAD$ and $FQ$ scale estimates. To adjust the parameters of the algorithms, a selection procedure is proposed based on the complete knowledge of the data distribution model. Areas of suboptimal parameters are also determined in case of incomplete knowledge of the distribution model. It is concluded that the direct use of the Chebyshev inequality implies the classical $N$-sigma rule. With the non-classical Chebyshev inequality, a robust outlier detection method is obtained, which slightly outperforms other considered algorithms.
Keywords: anomaly; outlier detection; Chebyshev inequality; robustness. 
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M. A. Chepulis; G. L. Shevlyakov. On outlier detection with the chebyshev type inequalities. Journal of the Belarusian State University. Mathematics and Informatics, Tome 3 (2020), pp. 28-35. http://geodesic.mathdoc.fr/item/BGUMI_2020_3_a2/

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