DocumentCode :
3784438
Title :
Necessary and sufficient conditions for Bayes risk consistency of a recursive kernel classification rule (Corresp.)
Author :
W. Greblicki;M. Pawlak
Volume :
33
Issue :
3
fYear :
1987
Firstpage :
408
Lastpage :
412
Abstract :
It is shown that, for a nonparametric recursive kernel classification rule,\sum^{n}_{i=1}h^{d}(i)I_{ \{h(i) > \epsilon \} } / \sum^{n}_{j=1} h^{d} (j) \rightarrow 0 {\rm as} n \rightarrow \infty,all\epsilon > 0and\sum^{\infty}_{i=1}h^{d}(i)= \inftyconstitute a set of conditions which are not only sufficient but also necessary for weak and strong Bayes risk consistency of the rule. In this way, weak and strong consistencies are shown to be equivalent.
Journal_Title :
IEEE Transactions on Information Theory
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.1987.1057309
Filename :
1057309
Link To Document :
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