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A nonparametric test of fit of a parametric model


  • Kozek, Andrzej S.


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.

Suggested Citation

  • Kozek, Andrzej S., 1991. "A nonparametric test of fit of a parametric model," Journal of Multivariate Analysis, Elsevier, vol. 37(1), pages 66-75, April.
  • Handle: RePEc:eee:jmvana:v:37:y:1991:i:1:p:66-75

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    Cited by:

    1. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    2. Gonzalez Manteiga, W. & Vilar Fernandez, J. M., 1995. "Testing linear regression models using non-parametric regression estimators when errors are non-independent," Computational Statistics & Data Analysis, Elsevier, vol. 20(5), pages 521-541, November.
    3. González-Manteiga, Wenceslao & Quintela-del-Río, Alejandro & Vieu, Philippe, 2002. "A note on variable selection in nonparametric regression with dependent data," Statistics & Probability Letters, Elsevier, vol. 57(3), pages 259-268, April.


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