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\(k\)-depth-nearest neighbour method and its performance on skew-normal distributons. (English) Zbl 1292.62075

Summary: In the present paper we investigate performance of the \(k\)-depth-nearest classifier. This classifier, proposed recently by Vencálek, uses the concept of data depth to improve the classification method known as the \(k\)-nearest neighbour. Simulation study which is presented here deals with the two-class classification problem in which the considered distributions belong to the family of skewed normal distributions.

MSC:

62G30 Order statistics; empirical distribution functions
62H30 Classification and discrimination; cluster analysis (statistical aspects)

Software:

sn
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References:

[1] Azzalini, A., Della Valle, A.: The multivariate skew-normal distribution. Biometrika 83, 4 (1996), 715-726. · Zbl 0885.62062
[2] Azzalini, A. R: package sn: The skew-normal and skew-t distributions (version 0.4-6). , 2006.
[3] Hlubinka, D.: Výpravy do hlubin dat. Antoch, J., Dohnal, G. (eds.): Sborník prací 15. letní školy JČMF ROBUST 2008, JČMF, Praha, 2009, 97-130)
[4] Hubert, M., van der Veeken, S.: Fast and robust classifiers adjusted for skewness. Lechevallier, Y., Saporta, G. (eds.): COMPSTAT 2010: proceedings in computational statistics: 19th symposium held in Paris, France Springer, Heidelberg, 2010, 1135-1142.
[5] Li, J., Cuesta-Albertos, J. A., Liu, R. Y.: DD-classifier: nonparametric classification procedure based on DD-plot. Journal of the American Statistical Association 104, 498 (2012), 737-753. · Zbl 1261.62058
[6] Paindaveine, D., Van Bever, G.: Nonparametrically consistent depth-based classifiers. arXiv preprint arXiv:1204.2996, 2012. · Zbl 1359.62258
[7] Vencálek, O.: Concept of Data Depth and Its Applications. Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 50, 2 (2011), 111-119. · Zbl 1244.62048
[8] Vencálek, O.: Weighted data depth and depth based classification. PhD Thesis, MFF UK, Praha, 2011. · Zbl 1244.62048
[9] Vencálek, O.: New depth-based modification of the \(k\)-nearest neighbour method. Informační bulletin České statistické společnosti, (2013))
[10] Zuo, Y., Serfling, R.: General notion of statistical depth function. Annals of Statistics 28 (2000), 461-482. · Zbl 1106.62334
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