The DOI matches its Crossref record; 28 of the 28 references it cites were found in a registry or an index.
General notions of statistical depth function
Abstract
Statistical depth functions are being formulated ad hoc with increasing popularity in nonparametric inference for multivariate data. Here we introduce several general structures for depth functions, classify many existing examples as special cases, and establish results on the possession, or lack thereof, of four key properties desirable for depth functions in general. Roughly speaking, these properties may be described as: affine invariance, maximality at center, monotonicity relative to deepest point, and vanishing at infinity. This provides a more systematic basis for selection of a depth function. In particular, from these and other considerations it is found that the halfspace depth behaves very well overall in comparison with various competitors.
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Dataset Security for Machine Learning: Data Poisoning, Backdoor Attacks, and Defenses
Goldblum, M., Tsipras, D., Xie, C., Chen, X., Schwarzschild, A., Song, D., Madry, A., Li, B., & Goldstein, T. (2023) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2022.3162397 · Cited by 362
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Metadata
- Authors
- Serfling, R., & Zuo, Y.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2000-04-01
- Volume
- 28
- Issue
- 2
- Pages
- 461-482
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2016440615
- Cited by
- 819
- References
- 28
- FWCI
- 8.25
- Type
- journal article
- Language
- en
- Open access
- closed
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