| Title:
|
Concept of Data Depth and Its Applications (English) |
| Author:
|
Vencálek, Ondřej |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
50 |
| Issue:
|
2 |
| Year:
|
2011 |
| Pages:
|
111-119 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Data depth is an important concept of nonparametric approach to multivariate data analysis. The main aim of the paper is to review possible applications of the data depth, including outlier detection, robust and affine-equivariant estimates of location, rank tests for multivariate scale difference, control charts for multivariate processes, and depth-based classifiers solving discrimination problem. (English) |
| Keyword:
|
data depth |
| Keyword:
|
nonparametric multivariate analysis |
| Keyword:
|
applications |
| Keyword:
|
rank |
| MSC:
|
60D05 |
| MSC:
|
62G05 |
| MSC:
|
62G15 |
| MSC:
|
62H05 |
| idZBL:
|
Zbl 1244.62048 |
| idMR:
|
MR2920713 |
| . |
| Date available:
|
2011-12-16T14:53:40Z |
| Last updated:
|
2013-09-18 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141759 |
| . |
| Reference:
|
[1] Donoho, D. L., Gasko, M.: Breakdown properties of location estimates based on halfspace depth and projected outlyingness. Annals of Statistics 20 (1992), 1803–1827. Zbl 0776.62031, MR 1193313, 10.1214/aos/1176348890 |
| Reference:
|
[2] Ghosh, A. K., Chaudhuri, P.: On Maximum Depth and Related Classifiers.. Scandinavian Journal of Statistics 32 (2005), 327–350. MR 2188677, 10.1111/j.1467-9469.2005.00423.x |
| Reference:
|
[3] Liu, R. Y.: Control charts for multivariate processes.. Journal of the American Statistical Association 90 (1995), 1380–1387. Zbl 0868.62075, MR 1379481, 10.1080/01621459.1995.10476643 |
| Reference:
|
[4] Liu, R. Y., Singh, K.: Rank tests for multivariate scale difference based on data depth. In: Liu, R. Y., Serfling, R., Souvaine, D. L. (eds.) DIMACS; Robust Multivariate Analysis, Computational Geometry and Applications American Mathematical Society, 2006, 17–34. MR 2343110 |
| Reference:
|
[5] Liu, R. Y., Parelius, J. M., Singh, K.: Multivariate analysis by data depth: Descriptive statistics, graphics and inference (with discussion). Annals of Statistics 27 (1999), 783–858. MR 1724033, 10.1214/aos/1018031259 |
| Reference:
|
[6] Rousseeuw, P. J., Ruts, I., Tukey, J.: The bagplot: a bivariate boxplot. The American Statistician 53 (1999), 382–387. |
| Reference:
|
[7] Tukey, J.: Mathematics and picturing data. Proceedings of the 1975 International Congress of Mathematics 2 (1975), 523–531. MR 0426989 |
| Reference:
|
[8] Zuo, Y., Serfling, R.: General notion of statistical depth function. Annals of Statistics 28 (2000), 461–482. MR 1790005, 10.1214/aos/1016218226 |
| . |
