Research of properties of the extrapolation depth functions using kernel density estimates

1Galkin, OA
1Taras Shevchenko National University of Kyiv
Dopov. Nac. akad. nauk Ukr. 2016, 7:27-32
https://doi.org/10.15407/dopovidi2016.07.027
Section: Information Science and Cybernetics
Language: Ukrainian
Abstract: 

The mathematical apparatus, which is intended for the research and solving the multiclass classification problems based on the use of the extrapolation depth functions, is developed. The properties of the extrapolation depth functions, which allow one to obtain some nonparametric classifier resistant to outliers that is able to bypass objects with zero depth, are studied. Nonparametric criteria to define and to build a multilevel smoothing structure, which enables one to obtain the global properties of density functions and the boundaries of classes under appropriate conditions of regularity, are studied.

Keywords: bayesian risk, extrapolation depth function, kernel density estimates
References: 
  1. Rousseeum P. J., Struyf A. Statist. Plann. Inference, 2004, 122: 163–170.
  2. Pollard D. Convergence of Stochastic Processes, New York: Springer, 1984. https://doi.org/10.1007/978-1-4612-5254-2
  3. Galkin O. A. Problems of Control and Informatics, 2015, No 5: 85–92 (in Russian).
  4. Zuo Y. J. Annals of Statistics, 2003, 31: 1463–1484. https://doi.org/10.1214/aos/1065705115
  5. Chacon J. I., Duong T., Wand M. P. Statist, 2011, 21: 810–837.