- Mahalanobis Depth
- Half Space Depth
- Projection Depth
- Simplicial Depth
Note: Mahalanobis depth does not do well for elliptical and non-elliptical distributions, projection depth is ideal for elliptical distributions while half-space or simplicial depths do well for non-elliptical distributions.
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Liu, R. (1990), “On a Notion of Data Depth Based on Random Simplices,” The Annals of Statistics, 18, 405–414.
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Liu, R. (1992), “Data Depth and Multivariate Rank Tests,” in L1-Statistical Analysis and Related Methods, ed. Y. Dodge, Amsterdam: North-Holland, pp. 279–294.
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Liu, R., Parelius, J., and Singh, K. (1999), “Multivariate Analysis by Data Depth: Descriptive Statistics, Graphics and Inference" (with discussion), Ann. Statist. Volume 27, Number 3 (1999), 783-858. doi:10.1214/aos/1018031260
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Jun Li , Juan A. Cuesta-Albertos & Regina Y. Liu (2012) DD-Classifier: Nonparametric Classification Procedure Based on DD-Plot, JASA, 107:498, 737-753, doi:10.1080/01621459.2012.688462
In this article, we use Mahalanobis depth to cover the well-studied Gaussian case, and half-space depth, simplicial depth, and projection depth to explore the robustness aspect of our approach. The last three depths are geometric and thus completely nonparametric.