| Title:
|
$k$-Depth-nearest Neighbour Method and its Performance on Skew-normal Distributons (English) |
| Author:
|
Vencálek, Ondřej |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
52 |
| Issue:
|
2 |
| Year:
|
2013 |
| Pages:
|
121-129 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
data depth |
| Keyword:
|
classification |
| Keyword:
|
k-nearest neighbour |
| Keyword:
|
skewed normal distribution |
| MSC:
|
62G30 |
| MSC:
|
62H30 |
| idZBL:
|
Zbl 06296020 |
| idMR:
|
MR3202385 |
| . |
| Date available:
|
2013-12-18T15:26:31Z |
| Last updated:
|
2014-07-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143544 |
| . |
| Reference:
|
[1] Azzalini, A., Della Valle, A.: The multivariate skew-normal distribution. Biometrika 83, 4 (1996), 715–726. MR 1440039, 10.1093/biomet/83.4.715 |
| Reference:
|
[2] Azzalini, A. R: package sn: The skew-normal and skew-t distributions (version 0.4-6). http://azzalini.stat.unipd.it/SN, 2006. |
| Reference:
|
[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). |
| Reference:
|
[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. |
| Reference:
|
[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, MR 2980081, 10.1080/01621459.2012.688462 |
| Reference:
|
[6] Paindaveine, D., Van Bever, G.: Nonparametrically consistent depth-based classifiers. arXiv preprint arXiv:1204.2996, 2012. |
| Reference:
|
[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, MR 2920713 |
| Reference:
|
[8] Vencálek, O.: Weighted data depth and depth based classification. PhD Thesis, MFF UK, Praha, 2011. |
| Reference:
|
[9] Vencálek, O.: New depth-based modification of the $k$-nearest neighbour method. Informační bulletin České statistické společnosti, (2013), (to appear). |
| Reference:
|
[10] Zuo, Y., Serfling, R.: General notion of statistical depth function. Annals of Statistics 28 (2000), 461–482. MR 1790005, 10.1214/aos/1016218226 |
| . |
