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Kernel regression estimation for incomplete data with applications

Author

Listed:
  • Majid Mojirsheibani

    (California State University)

  • Timothy Reese

    (California State University)

Abstract

Methods are proposed to construct kernel estimators of a regression function in the presence of incomplete data. Furthermore, exponential upper bounds are derived on the performance of the $$L_p$$ L p norms of the proposed estimators, which can then be used to establish various strong convergence results. The presence of incomplete data points are handled by a Horvitz–Thompson-type inverse weighting approach, where the unknown selection probabilities are estimated by both kernel regression and least-squares methods. As an immediate application of these results, the problem of nonparametric classification with partially observed data will be studied.

Suggested Citation

  • Majid Mojirsheibani & Timothy Reese, 2017. "Kernel regression estimation for incomplete data with applications," Statistical Papers, Springer, vol. 58(1), pages 185-209, March.
    • Handle: RePEc:spr:stpapr:v:58:y:2017:i:1:d:10.1007_s00362-015-0693-z
    DOI: 10.1007/s00362-015-0693-z
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    References listed on IDEAS

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    Cited by:

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    2. Mojirsheibani, Majid & Shaw, Crystal, 2018. "Classification with incomplete functional covariates," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 40-46.
    3. Li Cai & Suojin Wang, 2021. "Global statistical inference for the difference between two regression mean curves with covariates possibly partially missing," Statistical Papers, Springer, vol. 62(6), pages 2573-2602, December.
    4. Mojirsheibani, Majid, 2021. "On classification with nonignorable missing data," Journal of Multivariate Analysis, Elsevier, vol. 184(C).

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