Using local linear kernel smoothers to test the lack of fit of nonlinear regression models

Research output: Contribution to journalArticle

5 Scopus citations


Herein, we propose a data-driven test that assesses the lack of fit of nonlinear regression models. The comparison of local linear kernel and parametric fits is the basis of this test, and specific boundary-corrected kernels are not needed at the boundary when local linear fitting is used. Under the parametric null model, the asymptotically optimal bandwidth can be used for bandwidth selection. This selection method leads to the data-driven test that has a limiting normal distribution under the null hypothesis and is consistent against any fixed alternative. The finite-sample property of the proposed data-driven test is illustrated, and the power of the test is compared with that of some existing tests via simulation studies. We illustrate the practicality of the proposed test by using two data sets.

Original languageEnglish (US)
Pages (from-to)267-284
Number of pages18
JournalStatistical Methodology
Issue number4
Publication statusPublished - Dec 2005
Externally publishedYes



  • Bandwidth selection
  • Boundary effects
  • Fit comparison
  • Local linear kernel estimator

ASJC Scopus subject areas

  • Statistics and Probability

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