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On nonparametric classification with missing covariates

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  • Mojirsheibani, Majid
  • Montazeri, Zahra

Abstract

General procedures are proposed for nonparametric classification in the presence of missing covariates. Both kernel-based imputation as well as Horvitz-Thompson-type inverse weighting approaches are employed to handle the presence of missing covariates. In the case of imputation, it is a certain regression function which is being imputed (and not the missing values). Using the theory of empirical processes, the performance of the resulting classifiers is assessed by obtaining exponential bounds on the deviations of their conditional errors from that of the Bayes classifier. These bounds, in conjunction with the Borel-Cantelli lemma, immediately provide various strong consistency results.

Suggested Citation

  • Mojirsheibani, Majid & Montazeri, Zahra, 2007. "On nonparametric classification with missing covariates," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 1051-1071, May.
  • Handle: RePEc:eee:jmvana:v:98:y:2007:i:5:p:1051-1071
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    References listed on IDEAS

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    1. Hazelton, Martin L., 2000. "Marginal density estimation from incomplete bivariate data," Statistics & Probability Letters, Elsevier, vol. 47(1), pages 75-84, March.
    2. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, July.
    3. Wang Q. & Linton O. & Hardle W., 2004. "Semiparametric Regression Analysis With Missing Response at Random," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 334-345, January.
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