Kernel classification rules in the presence of missing values

The nonparametric kernel classification rule derived from incomplete data is studied. Methods of designing kernel decision rules possessing optimal asymptotic properties are proposed. Consistency and rates of convergence are examined. It is argued that the replacement methods using the regression approach can lead to the inconsistency of resulting decision rules. On the other hand, a method employing the concept of predictive density yields asymptotically optimal classification rules.<<ETX>>

[1]  Anil K. Jain,et al.  Classifier design with Parzen Windows , 1988 .

[2]  L. Devroye,et al.  Distribution-Free Consistency Results in Nonparametric Discrimination and Regression Function Estimation , 1980 .

[3]  J. Marron.  Optimal Rates of Convergence to Bayes Risk in Nonparametric Discrimination , 1983 .

[4]  Miroslaw Pawlak,et al.  Necessary and sufficient conditions for Bayes risk consistency of a recursive kernel classification rule , 1987, IEEE Trans. Inf. Theory.

[5]  Adam Krzyzak,et al.  Distribution-free consistency of a nonparametric kernel regression estimate and classification , 1984, IEEE Trans. Inf. Theory.

[6]  Prakasa Rao.  Nonparametric functional estimation , 1983 .

[7]  David J. Hand,et al.  Kernel Discriminant Analysis , 1983 .

[8]  Wlodzimierz Greblicki,et al.  Asymptotically optimal pattern recognition procedures with density estimates (Corresp.) , 1978, IEEE Trans. Inf. Theory.

[9]  Roderick J. A. Little,et al.  Consistent Regression Methods for Discriminant Analysis with Incomplete Data , 1978 .

[10]  John K. Dixon,et al.  Pattern Recognition with Partly Missing Data , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[11]  D. M. Titterington,et al.  Kernel‐Based Density Estimates from Incomplete Data , 1983 .

[12]  Seymour Geisser,et al.  4 Bayesian discrimination , 1982, Classification, Pattern Recognition and Reduction of Dimensionality.

[13]  Olive Jean Dunn,et al.  Alternative Approaches to Missing Values in Discriminant Analysis , 1976 .

[14]  E. S. Gelsema,et al.  Incomplete Data Sets , 1988 .