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Smoothing for Discrete Kernels in Discrimination
Author(s) -
Tutz Gerhard
Publication year - 1988
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710300617
Subject(s) - consistency (knowledge bases) , smoothing , maximization , mathematics , kernel (algebra) , bayes' theorem , multivariate statistics , statistics , econometrics , mathematical optimization , bayesian probability , combinatorics , discrete mathematics
In multivariate discrimination by the discrete kernel method the allocation rule is Bayes risk consistent if the smoothing parameter is chosen by maximization of the leaving‐one‐out nonerror rate. It is shown that consistency still holds if the leaving‐one‐out nonerror rate is replaced by a smoothed version. Thus a cross‐validatory criterion is given which secures consistency and really can be used in practice.