Nonparametric check for partial linear errors-in-covariables models with validation data

Wangli Xu*, Lixing ZHU

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

8 Citations (Scopus)


In this paper, we investigate the goodness-of-fit test of partial linear regression models when the true variable in the linear part is not observable but the surrogate variable $$\tilde{X}$$X~, the variable in the non-linear part $$T$$T and the response $$Y$$Y are exactly measured. In addition, an independent validation data set for $$X$$X is available. By a transformation, it is found that we only need to check whether the linear model is plausible or not. We estimate the conditional expectation of $$X$$X under a given the surrogate variable with the help of the validation sample. Finally, a residual-based empirical test for the partial linear models is constructed. A nonparametric Monte Carlo test procedure is used, and the null distribution can be well approximated even when data are from alternative models converging to the hypothetical model. Simulation results show that the proposed method works well.

Original languageEnglish
Pages (from-to)793-815
Number of pages23
JournalAnnals of the Institute of Statistical Mathematics
Issue number4
Publication statusPublished - 22 Aug 2015

Scopus Subject Areas

  • Statistics and Probability

User-Defined Keywords

  • Errors-in-variables model
  • Goodness-of-fit testing
  • Partial linear models
  • Validation sample


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