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Pairwise local Fisher and naive Bayes: improving two standard discriminants. (English) Zbl 1456.62062
Summary: The Fisher discriminant is probably the best known likelihood discriminant for continuous data. Another benchmark discriminant is the naive Bayes, which is based on marginals only. In this paper we extend both discriminants by modeling dependence between pairs of variables. In the continuous case this is done by local Gaussian versions of the Fisher discriminant. In the discrete case the naive Bayes is extended by taking geometric averages of pairwise joint probabilities. We also indicate how the two approaches can be combined for mixed continuous and discrete data. The new discriminants show promising results in a number of simulation experiments and real data illustrations.
62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
62H30 Classification and discrimination; cluster analysis (statistical aspects)
62P20 Applications of statistics to economics
gamair; lg; localgauss; np; R
Full Text: DOI
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