Empirical likelihood inference in nonlinear errors-in-covariables models with validation data

Winfried Stute*, Liugen Xue, Lixing ZHU

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

46 Citations (Scopus)


In this article we study inference in parametric-nonparametric errors-in-covariables regression models using an empirical likelihood approach based on validation data. It is shown that the asymptotic behavior of the proposed estimator depends on the ratio of the sizes of the primary sample and the validation sample, respectively. Unlike cases without measurement errors, the limit distribution of the estimator is no longer tractable and cannot be used for constructing confidence regions. Monte Carlo approximations are employed to simulate the limit distribution. To increase the coverage accuracy of confidence regions, two adjusted empirical likelihood estimators are recommended, which in the limit have a standard chi-squared distribution. A simulation study is carried out to compare the proposed methods with other existing methods. The new methods outperform the least squares method, and one of them works better than simulation-extrapolation (SIMEX) estimation, even when the restrictive model assumptions needed for SIMEX are satisfied. An application to a real dataset illustrates our new approach.

Original languageEnglish
Pages (from-to)332-346
Number of pages15
JournalJournal of the American Statistical Association
Issue number477
Publication statusPublished - Mar 2007

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Confidence regions: Empirical likelihood
  • Errors in covariahles: Nnnpurametric estimation
  • Validation data


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