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Empirical likelihood and Wilks phenomenon for data with nonignorable missing values

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  • Puying Zhao
  • Lei Wang
  • Jun Shao

Abstract

Wilks's theorem is useful for constructing confidence regions. When applying the popular empirical likelihood to data with nonignorable nonresponses, Wilks's phenomenon does not hold. This paper unveils that this is caused by the extra estimation of the nuisance parameter in the nonignorable nonresponse propensity. Motivated by this result, we propose an adjusted empirical likelihood for which Wilks's theorem holds. Asymptotic results are presented and supplemented by simulation results for finite sample performance of the point estimators and confidence regions. An analysis of a data set is included for illustration.

Suggested Citation

  • Puying Zhao & Lei Wang & Jun Shao, 2019. "Empirical likelihood and Wilks phenomenon for data with nonignorable missing values," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 46(4), pages 1003-1024, December.
    • Handle: RePEc:bla:scjsta:v:46:y:2019:i:4:p:1003-1024
    DOI: 10.1111/sjos.12379
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    Cited by:

    1. Mojirsheibani, Majid, 2021. "On classification with nonignorable missing data," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    2. Majid Mojirsheibani, 2022. "On the maximal deviation of kernel regression estimators with NMAR response variables," Statistical Papers, Springer, vol. 63(5), pages 1677-1705, October.
    3. Wang, Lei & Zhao, Puying & Shao, Jun, 2021. "Dimension-reduced semiparametric estimation of distribution functions and quantiles with nonignorable nonresponse," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).

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