Robust estimation of distribution functions and quantiles with non-ignorable missing data

Pu Ying Zhao, Man Lai TANG, Nian Sheng Tang*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

15 Citations (Scopus)


This paper considers several robust estimators for distribution functions and quantiles of a response variable when some responses may not be observed under the non-ignorable missing data mechanism. Based on a particular semiparametric regression model for non-ignorable missing response, we propose a nonparametric/semiparametric estimation method and an augmented inverse probability weighted imputation method to estimate the distribution function and quantiles of a response variable. Under some regularity conditions, we derive asymptotic properties of the proposed distribution function and quantile estimators. Two empirical log-likelihood functions are also defined to construct confidence intervals for distribution function of a response variable. Simulation studies show that our proposed methods are robust. In particular, the semiparametric estimator is more efficient than the nonparametric estimator, and the inverse probability weighted imputation estimator is bias-corrected.

Original languageEnglish
Pages (from-to)575-595
Number of pages21
JournalCanadian Journal of Statistics
Issue number4
Publication statusPublished - Dec 2013

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Distribution estimation
  • Exponential tilting
  • Non-ignorable missing
  • Nonparametric regression
  • Quantile estimation


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