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The Glivenko-Cantelli theorem based on data with randomly imputed missing values

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  • Mojirsheibani, Majid

Abstract

Glivenko-Cantelli-type results will be derived for the performance of the empirical distribution function under imputation of the missing data in the univariate case, when there are no auxiliary covariates. According to these results, both random imputation and the adjusted random imputation produce reliable estimates of the unknown distribution function. They are reliable in the sense that the corresponding empirical distribution functions stay (w.p.1) "close" to F(t), uniformly over t. At the same time, it is also shown that if r(n)[less-than-or-equals, slant]n is the number of nonmissing observations, then one cannot improve on the performance of the empirical distribution function Fr(n) by generating artificial data, in order to increase the sample size from r(n) to n (using either one of the above two imputation procedures).

Suggested Citation

  • Mojirsheibani, Majid, 2001. "The Glivenko-Cantelli theorem based on data with randomly imputed missing values," Statistics & Probability Letters, Elsevier, vol. 55(4), pages 385-396, December.
  • Handle: RePEc:eee:stapro:v:55:y:2001:i:4:p:385-396
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    References listed on IDEAS

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    1. Arenal-Gutiérrez, Eusebio & Matrán, Carlos & Cuesta-Albertos, Juan A., 1996. "Unconditional Glivenko-Cantelli-type theorems and weak laws of large numbers for bootstrap," Statistics & Probability Letters, Elsevier, vol. 26(4), pages 365-375, March.
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    Cited by:

    1. Yang, Hanfang & Zhao, Yichuan, 2015. "Smoothed jackknife empirical likelihood inference for ROC curves with missing data," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 123-138.

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