Journal of Systems Science and Complexity

, Volume 31, Issue 3, pp 820–840 | Cite as

Adjusted Empirical Likelihood Estimation of Distribution Function and Quantile with Nonignorable Missing Data

  • Xianwen Ding
  • Niansheng Tang


This paper considers the estimation problem of distribution functions and quantiles with nonignorable missing response data. Three approaches are developed to estimate distribution functions and quantiles, i.e., the Horvtiz-Thompson-type method, regression imputation method and augmented inverse probability weighted approach. The propensity score is specified by a semiparametric exponential tilting model. To estimate the tilting parameter in the propensity score, the authors propose an adjusted empirical likelihood method to deal with the over-identified system. Under some regular conditions, the authors investigate the asymptotic properties of the proposed three estimators for distribution functions and quantiles, and find that these estimators have the same asymptotic variance. The jackknife method is employed to consistently estimate the asymptotic variances. Simulation studies are conducted to investigate the finite sample performance of the proposed methodologies.


Adjusted empirical likelihood distribution estimation exponential tilting model nonignorable missing data quantile 


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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Key Laboratory of Statistical Modeling & Data Analysis of Yunnan ProvinceYunnan UniversityKunmingChina
  2. 2.Department of MathematicsJiangsu University of TechnologyChangzhouChina

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