Empirical likelihood inference in linear regression with nonignorable missing response

Cuizhen Niu, Xu Guo, Wangli Xu*, Lixing ZHU

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

22 Citations (Scopus)


Parameter estimation for nonignorable nonresponse data is a challenging issue as the missing mechanism is unverified in practice and the parameters of response probabilities need to be estimated. This article aims at applying the empirical likelihood to construct the confidence intervals for the parameters of interest in linear regression models with nonignorable missing response data and the nonignorable missing mechanism is specified as an exponential tilting model. Three empirical likelihood ratio functions based on weighted empirical likelihood and imputed empirical likelihood are defined. It is proved that, except one that is chi-squared distributed, all the others are asymptotically weighted chi-squared distributed whenever the tilting parameter is either given or estimated. The asymptotic normality for the related parameter estimates is also investigated. Simulation studies are conducted to evaluate the finite sample performance of the proposed estimates in terms of coverage probabilities and average widths for the confidence intervals of parameters. A real data analysis is analyzed for illustration.

Original languageEnglish
Pages (from-to)91-112
Number of pages22
JournalComputational Statistics and Data Analysis
Publication statusPublished - Nov 2014

Scopus Subject Areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Empirical likelihood inference
  • Imputed empirical likelihood
  • Inverse probability weighted
  • Linear regression
  • Nonignorable missing response


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