Kernel classification rules from missing data

Nonparametric kernel classification rules derived from incomplete (missing) data are studied. A number of techniques of handling missing observation in the training set are taken into account. In particular, the straightforward approach of designing a classifier only from available data (deleting missing values) is considered. The class of imputation techniques is also taken into consideration. In the latter case, one estimates missing values and then calculates classification rules from such a completed training set. Consistency and speed of convergence of proposed classification rules are established. Results of simulation studies are presented. >

[1]  B. Silverman.  Density estimation for statistics and data analysis , 1986 .

[2]  Roderick J. A. Little,et al.  Statistical Analysis with Missing Data , 1988 .

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

[4]  W. Hoeffding.  Probability Inequalities for sums of Bounded Random Variables , 1963 .

[5]  S. Yakowitz.  Nonparametric Density Estimation, Prediction, and Regression for Markov Sequences , 1985 .

[6]  John Van Ness,et al.  On the dominance of non-parametric Bayes rule discriminant algorithms in high dimensions , 1980, Pattern Recognit..

[7]  Matt P. Wand,et al.  Minimizing L 1 distance in nonparametric density estimation , 1988 .

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

[9]  Adam Krzyzak,et al.  The rates of convergence of kernel regression estimates and classification rules , 1986, IEEE Trans. Inf. Theory.

[10]  Richard L. Wheeden.  Measure and integral , 1977 .

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

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

[13]  Josef Kittler.  Classification of Incomplete Pattern Vectors Using Modified Discrminant Functions , 1978, IEEE Transactions on Computers.

[14]  M. Pawlak.  On the almost everywhere properties of the kernel regression estimate , 1991 .

[15]  Elias Masry.  Nonparametric estimation of conditional probability densities and expectations of stationary processes: strong consistency and rates , 1989 .

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

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

[18]  Miroslaw Pawlak,et al.  Almost sure convergence of classification procedures using Hermite series density estimates , 1983, Pattern Recognit. Lett..

[19]  J. Marron.  Automatic smoothing parameter selection: A survey , 1988 .

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

[21]  D. M. Titterington,et al.  Imputation of missing values using density estimation , 1989 .

[22]  Qiuming Zhu.  On the minimum probability of error of classification with incomplete patterns , 1990, Pattern Recognit..

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

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

[25]  C. J. Stone,et al.  Consistent Nonparametric Regression , 1977 .

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