Research of nonparametric maximum-depth classifiers based on the spatial quantiles - Galkin, O. A. (Reports of the National Academy of Sciences of Ukraine, 2015)
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.