# On Maximum Depth and Related Classifiers

## Author

Listed:
• ANIL K. GHOSH
• PROBAL CHAUDHURI

## Abstract

. Over the last couple of decades, data depth has emerged as a powerful exploratory and inferential tool for multivariate data analysis with wide‐spread applications. This paper investigates the possible use of different notions of data depth in non‐parametric discriminant analysis. First, we consider the situation where the prior probabilities of the competing populations are all equal and investigate classifiers that assign an observation to the population with respect to which it has the maximum location depth. We propose a different depth‐based classification technique for unequal prior problems, which is also useful for equal prior cases, especially when the populations have different scatters and shapes. We use some simulated data sets as well as some benchmark real examples to evaluate the performance of these depth‐based classifiers. Large sample behaviour of the misclassification rates of these depth‐based non‐parametric classifiers have been derived under appropriate regularity conditions.

## Suggested Citation

• Anil K. Ghosh & Probal Chaudhuri, 2005. "On Maximum Depth and Related Classifiers," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(2), pages 327-350, June.
• Handle: RePEc:bla:scjsta:v:32:y:2005:i:2:p:327-350
DOI: 10.1111/j.1467-9469.2005.00423.x
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File URL: https://doi.org/10.1111/j.1467-9469.2005.00423.x

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## Citations

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Cited by:

1. repec:hal:spmain:info:hdl:2441/64itsev5509q8aa5mrbhi0g0b6 is not listed on IDEAS
2. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434, arXiv.org, revised Sep 2015.
3. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434, arXiv.org, revised Sep 2015.
4. Vencalek, Ondrej & Pokotylo, Oleksii, 2018. "Depth-weighted Bayes classification," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 1-12.
5. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434, arXiv.org, revised Sep 2015.
6. repec:hal:spmain:info:hdl:2441/3qnaslliat80pbqa8t90240unj is not listed on IDEAS
7. Nedret Billor & Asheber Abebe & Asuman Turkmen & Sai Nudurupati, 2008. "Classification Based on Depth Transvariations," Journal of Classification, Springer;The Classification Society, vol. 25(2), pages 249-260, November.
8. Dag Kolsrud, 2015. "A Time‐Simultaneous Prediction Box for a Multivariate Time Series," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 34(8), pages 675-693, December.
9. Subhajit Dutta & Anil Ghosh, 2012. "On robust classification using projection depth," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(3), pages 657-676, June.
10. Yonggang Hu & Yong Wang & Yi Wu & Qiang Li & Chenping Hou, 2011. "Generalized Mahalanobis depth in the reproducing kernel Hilbert space," Statistical Papers, Springer, vol. 52(3), pages 511-522, August.
11. Ye Dong & Stephen Lee, 2014. "Depth functions as measures of representativeness," Statistical Papers, Springer, vol. 55(4), pages 1079-1105, November.
12. Mia Hubert & Stephan Van der Veeken, 2010. "Robust classification for skewed data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 4(4), pages 239-254, December.
13. Daniel Hlubinka & Irène Gijbels & Marek Omelka & Stanislav Nagy, 2015. "Integrated data depth for smooth functions and its application in supervised classification," Computational Statistics, Springer, vol. 30(4), pages 1011-1031, December.
14. J. A. Cuesta-Albertos & M. Febrero-Bande & M. Oviedo de la Fuente, 2017. "The $$\hbox {DD}^G$$ DD G -classifier in the functional setting," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 119-142, March.
15. López Pintado, Sara & Romo, Juan, 2005. "Depth-based classification for functional data," DES - Working Papers. Statistics and Econometrics. WS ws055611, Universidad Carlos III de Madrid. Departamento de Estadística.
16. Olusola Samuel Makinde, 2019. "Classification rules based on distribution functions of functional depth," Statistical Papers, Springer, vol. 60(3), pages 629-640, June.
17. Tatjana Lange & Karl Mosler & Pavlo Mozharovskyi, 2014. "Fast nonparametric classification based on data depth," Statistical Papers, Springer, vol. 55(1), pages 49-69, February.
18. Ondrej Vencalek & Olusola Samuel Makinde, 2021. "RR-classifier: a nonparametric classification procedure in multidimensional space based on relative ranks," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(4), pages 675-693, December.
19. Anirvan Chakraborty & Probal Chaudhuri, 2014. "On data depth in infinite dimensional spaces," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 303-324, April.
20. Davy Paindaveine & Germain Van Bever, 2017. "Halfspace Depths for Scatter, Concentration and Shape Matrices," Working Papers ECARES ECARES 2017-19, ULB -- Universite Libre de Bruxelles.
21. Daouia, Abdelaati & Paindaveine, Davy, 2019. "Multivariate Expectiles, Expectile Depth and Multiple-Output Expectile Regression," TSE Working Papers 19-1022, Toulouse School of Economics (TSE), revised Feb 2023.
22. Pritha Guha, 2018. "Application of Multivariate-Rank-Based Techniques in Clustering of Big Data," Vikalpa: The Journal for Decision Makers, , vol. 43(4), pages 179-190, December.
23. Karl Mosler & Pavlo Mozharovskyi, 2017. "Fast DD-classification of functional data," Statistical Papers, Springer, vol. 58(4), pages 1055-1089, December.
24. Mia Hubert & Peter Rousseeuw & Pieter Segaert, 2017. "Multivariate and functional classification using depth and distance," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 11(3), pages 445-466, September.

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