A nonparametric test of fit of a parametric model

Andrzej S. Kozek*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


We propose a natural test of fit of a parametric regression model. The test is based on a comparison of a nonparametric kernel estimate of a regression function with its least-squares parametric estimate. Under the null hypothesis we derive approximations to the probability distribution functions of the test statistic. The approximations are exact with a power rate. Moreover, we prove the consistency of the test.

Original languageEnglish
Pages (from-to)66-75
Number of pages10
JournalJournal of Multivariate Analysis
Issue number1
Publication statusPublished - 1991
Externally publishedYes


  • least squares method
  • maximum deviation distribution
  • nonlinear regression
  • nonparametric regression
  • parametric regression
  • test of fit


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