Research of nonparametric maximum-depth classifiers based on the spatial quantiles
DOI:
https://doi.org/10.15407/dopovidi2015.10.021Keywords:
Bayes risk, spatial depth, spatial quantilesAbstract
A nonparametric approach is proposed to solve the recognition problems, when separating surfaces cannot effectively be approximated by finite-parametric linear or quadratic functions. The approach is based on a function of the spatial depth, which is computationally less expensive and can be used for pattern recognition problems in an infinite-dimensional Hilbert space. A depth-based classifier is built on the basis of the concept of spatial quantiles. The properties of optimality are investigated in the case where the a posteriori probabilities of competing elliptical sets are equal. The uniform convergence of the spatial depth function is studied, and the estimates of the effectiveness of maximum depth classifiers are calculated.
Downloads
References
Jornsten R., Vardi Y., Zhang C. H. Statistical data Analysis, 2002: 354–365.
Chaudhuri P. J. of the American Statistical Association, 1996, 91: 864–870. https://doi.org/10.1080/01621459.1996.10476954
Zuo Y., Serfling R. The Annals of Statistics, 2000, 28: 463–481.
Lachenbruch P., Mickey M. Technometrics, 1968, 10: 3–10.
Silverman B. W. Density estimation for Statistics and Data Analysis, London: Chapman and Hall, 1986: 1–7. https://doi.org/10.1007/978-1-4899-3324-9_1
Godtliebsen F., Marron J. S., Chaudhuri P. J. of Computational and Graphical Statistics, 2002, 11: 3–21. https://doi.org/10.1198/106186002317375596
Zuo Y., Serfling R. The Annals of Statistics, 2000, 28: 484–497.
Nolan D. Stochastic Processes and Applications, 1992, 42: 159–167. https://doi.org/10.1016/0304-4149(92)90032-L
Koltchinskii V. I. The Annals of Statistics, 1997, 25: 439–474. https://doi.org/10.1214/aos/1031833659
Serfling R. A depth function and a scale curve based on spatial depth, Boston: Birkhaeuser, 2002: 27–36.
Holmes C. C., Adams N.M. J. of the Royal Statistical Society, 2002, 64: 297–304.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Reports of the National Academy of Sciences of Ukraine
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
