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

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Abstract

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.

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Authors and Affiliations

  1. Key Laboratory of Statistical Modeling & Data Analysis of Yunnan Province, Yunnan University, Kunming, 650500, China

    Xianwen Ding & Niansheng Tang

  2. Department of Mathematics, Jiangsu University of Technology, Changzhou, 213001, China

    Xianwen Ding

Authors
  1. Xianwen Ding
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  2. Niansheng Tang
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Corresponding author

Correspondence to Xianwen Ding.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 11671349 and 11601195, the Scientific Research Innovation Team of Yunnan Province under Grant No. 2015HC028, and the Natural Science Foundation of Jiangsu Province of China under Grant No. BK20160289.

This paper was recommended for publication by Editor SHAO Jun.

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Ding, X., Tang, N. Adjusted Empirical Likelihood Estimation of Distribution Function and Quantile with Nonignorable Missing Data. J Syst Sci Complex 31, 820–840 (2018). https://doi.org/10.1007/s11424-018-6334-6

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  • DOI: https://doi.org/10.1007/s11424-018-6334-6

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