We study a class of decision rules based on an adaptive partitioning of an Euclidean observation space. The class of partitions has a computationally attractive form, and the related decision rule is invariant under strictly monotone transformations of coordinate axes. We provide sufficient conditions that a sequence of decision rules be asymptotically Bayes risk efficient as sample size increases. The sufficient conditions involve no regularity assumptions on the underlying parent distributions.
@article{1176344197,
author = {Gordon, Louis and Olshen, Richard A.},
title = {Asymptotically Efficient Solutions to the Classification Problem},
journal = {Ann. Statist.},
volume = {6},
number = {1},
year = {1978},
pages = { 515-533},
language = {en},
url = {http://dml.mathdoc.fr/item/1176344197}
}
Gordon, Louis; Olshen, Richard A. Asymptotically Efficient Solutions to the Classification Problem. Ann. Statist., Tome 6 (1978) no. 1, pp. 515-533. http://gdmltest.u-ga.fr/item/1176344197/