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On the $$L_p$$ L p norms of kernel regression estimators for incomplete data with applications to classification

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  • Timothy Reese

    (California State University)

  • Majid Mojirsheibani

    (California State University)

Abstract

We consider kernel methods to construct nonparametric estimators of a regression function based on incomplete data. To tackle the presence of incomplete covariates, we employ Horvitz–Thompson-type inverse weighting techniques, where the weights are the selection probabilities. The unknown selection probabilities are themselves estimated using (1) kernel regression, when the functional form of these probabilities are completely unknown, and (2) the least-squares method, when the selection probabilities belong to a known class of candidate functions. To assess the overall performance of the proposed estimators, we establish exponential upper bounds on the $$L_p$$ L p norms, $$1\le p

Suggested Citation

  • Timothy Reese & Majid Mojirsheibani, 2017. "On the $$L_p$$ L p norms of kernel regression estimators for incomplete data with applications to classification," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(1), pages 81-112, March.
    • Handle: RePEc:spr:stmapp:v:26:y:2017:i:1:d:10.1007_s10260-016-0359-6
    DOI: 10.1007/s10260-016-0359-6
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    References listed on IDEAS

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    Cited by:

    1. Mojirsheibani, Majid & Shaw, Crystal, 2018. "Classification with incomplete functional covariates," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 40-46.
    2. Mojirsheibani, Majid, 2021. "On classification with nonignorable missing data," Journal of Multivariate Analysis, Elsevier, vol. 184(C).

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