Necessary and sufficient conditions for Bayes risk consistency of a recursive Kernal classification rule

Authors:
Wlodzimierz Greblicki;Miroslaw Pawlak
Affiliations:
Technical Univ. of Wroclaw, Wroclaw, Poland;The Univ. of Manitoba, Winnipeg, Canada
Venue:
IEEE Transactions on Information Theory
Year:
1987

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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,allepsilon > 0andsum^{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.