k -Depth-nearest Neighbour Method and its Performance on Skew-normal Distributons

Ondřej Vencálek

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2013)

  • Volume: 52, Issue: 2, page 121-129
  • ISSN: 0231-9721

Abstract

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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.

How to cite

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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 52.2 (2013): 121-129. <http://eudml.org/doc/260822>.

@article{Vencálek2013,
abstract = {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.},
author = {Vencálek, Ondřej},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {data depth; classification; k-nearest neighbour; skewed normal distribution; data depth; classification; -nearest neighbour; skewed normal distribution},
language = {eng},
number = {2},
pages = {121-129},
publisher = {Palacký University Olomouc},
title = {$k$-Depth-nearest Neighbour Method and its Performance on Skew-normal Distributons},
url = {http://eudml.org/doc/260822},
volume = {52},
year = {2013},
}

TY - JOUR
AU - Vencálek, Ondřej
TI - $k$-Depth-nearest Neighbour Method and its Performance on Skew-normal Distributons
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2013
PB - Palacký University Olomouc
VL - 52
IS - 2
SP - 121
EP - 129
AB - 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.
LA - eng
KW - data depth; classification; k-nearest neighbour; skewed normal distribution; data depth; classification; -nearest neighbour; skewed normal distribution
UR - http://eudml.org/doc/260822
ER -

References

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  1. Azzalini, A., Della Valle, A., 10.1093/biomet/83.4.715, Biometrika 83, 4 (1996), 715–726. (1996) MR1440039DOI10.1093/biomet/83.4.715
  2. Azzalini, A. R, package sn: The skew-normal and skew-t distributions (version 0.4-6), http://azzalini.stat.unipd.it/SN, 2006. (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). (2009) 
  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. (2010) 
  5. Li, J., Cuesta-Albertos, J. A., Liu, R. Y., 10.1080/01621459.2012.688462, Journal of the American Statistical Association 104, 498 (2012), 737–753. (2012) Zbl1261.62058MR2980081DOI10.1080/01621459.2012.688462
  6. Paindaveine, D., Van Bever, G., Nonparametrically consistent depth-based classifiers, arXiv preprint arXiv:1204.2996, 2012. (2012) 
  7. Vencálek, O., Concept of Data Depth and Its Applications, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 50, 2 (2011), 111–119. (2011) Zbl1244.62048MR2920713
  8. Vencálek, O., Weighted data depth and depth based classification, PhD Thesis, MFF UK, Praha, 2011. (2011) 
  9. Vencálek, O., New depth-based modification of the k -nearest neighbour method, Informační bulletin České statistické společnosti, (2013), (to appear). (2013) 
  10. Zuo, Y., Serfling, R., 10.1214/aos/1016218226, Annals of Statistics 28 (2000), 461–482. (2000) MR1790005DOI10.1214/aos/1016218226

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