$k$-Depth-nearest Neighbour Method and its Performance on Skew-normal Distributons
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 52 (2013) no. 2, pp. 121-129 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 62G30, 62H30
Keywords: data depth; classification; k-nearest neighbour; skewed normal distribution
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Vencálek, Ondřej. $k$-Depth-nearest Neighbour Method and its Performance on Skew-normal Distributons. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 52 (2013) no. 2, pp. 121-129. http://geodesic.mathdoc.fr/item/AUPO_2013_52_2_a10/

[1] Azzalini, A., Della Valle, A.: The multivariate skew-normal distribution. Biometrika 83, 4 (1996), 715–726. | DOI | MR

[2] Azzalini, A. R: package sn: The skew-normal and skew-t distributions (version 0.4-6). http://azzalini.stat.unipd.it/SN, 2006.

[3] Hlubinka, D.: Výpravy do hlubin dat. In: Antoch, J., Dohnal, G. (eds.): Sborník prací 15. letní školy JČMF ROBUST 2008, JČMF, Praha, 2009, 97–130, (in czech).

[4] Hubert, M., van der Veeken, S.: Fast and robust classifiers adjusted for skewness. In: 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. | DOI | MR | Zbl

[6] Paindaveine, D., Van Bever, G.: Nonparametrically consistent depth-based classifiers. arXiv preprint arXiv:1204.2996, 2012.

[7] Vencálek, O.: Concept of Data Depth and Its Applications. Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 50, 2 (2011), 111–119. | MR | Zbl

[8] Vencálek, O.: Weighted data depth and depth based classification. PhD Thesis, MFF UK, Praha, 2011.

[9] Vencálek, O.: New depth-based modification of the $k$-nearest neighbour method. Informační bulletin České statistické společnosti, (2013), (to appear).

[10] Zuo, Y., Serfling, R.: General notion of statistical depth function. Annals of Statistics 28 (2000), 461–482. | DOI | MR