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Goodness-of-fit test for linear models based on local polynomials

Author

Listed:
  • Alcalá, J. T.
  • Cristóbal, J. A.
  • González-Manteiga, W.

Abstract

We test if a regression function belongs to a class of parametric models by measuring the discrepancy between a parametric fit and a local polynomial regression. The proposed test is a weighted L2-norm of a smoothed function based on the parametric residuals.

Suggested Citation

  • Alcalá, J. T. & Cristóbal, J. A. & González-Manteiga, W., 1999. "Goodness-of-fit test for linear models based on local polynomials," Statistics & Probability Letters, Elsevier, vol. 42(1), pages 39-46, March.
    • Handle: RePEc:eee:stapro:v:42:y:1999:i:1:p:39-46
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    Citations

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    Cited by:

    1. Dette, Holger, 2000. "On a nonparametric test for linear relationships," Statistics & Probability Letters, Elsevier, vol. 46(3), pages 307-316, February.
    2. Mario Francisco-Fernández & Juan Vilar-Fernández, 2009. "Two tests for heteroscedasticity in nonparametric regression," Computational Statistics, Springer, vol. 24(1), pages 145-163, February.
    3. Gilles R. Ducharme & Bénédicte Fontez, 2004. "A Smooth Test of Goodness-of-Fit for Growth Curves and Monotonic Nonlinear Regression Models," Biometrics, The International Biometric Society, vol. 60(4), pages 977-986, December.
    4. Biedermann, Stefanie & Dette, Holger, 2000. "Testing linearity of regression models with dependent errors by kernel based methods," Technical Reports 2000,40, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    5. J. Opsomer & M. Francisco-Fernández, 2010. "Finding local departures from a parametric model using nonparametric regression," Statistical Papers, Springer, vol. 51(1), pages 69-84, January.
    6. Stefanie Biedermann & Holger Dette, 2000. "Testing linearity of regression models with dependent errors by kernel based methods," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 417-438, December.
    7. Heuchenne, Cédric & Van Keilegom, Ingrid, 2010. "Goodness-of-fit tests for the error distribution in nonparametric regression," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1942-1951, August.
    8. Hall, Peter & Park, Byeong U., 2004. "Bandwidth choice for local polynomial estimation of smooth boundaries," Journal of Multivariate Analysis, Elsevier, vol. 91(2), pages 240-261, November.
    9. Gijbels, Irène & Rousson, Valentin, 2001. "A nonparametric least-squares test for checking a polynomial relationship," Statistics & Probability Letters, Elsevier, vol. 51(3), pages 253-261, February.
    10. Dette, Holger & Neumeyer, Natalie, 2000. "Nonparametric analysis of covariance," Technical Reports 2000,42, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    11. Dette, Holger & Hetzler, Benjamin, 2004. "Specification tests indexed by bandwidths," Technical Reports 2004,48, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    12. J. Ojeda & J. Cristóbal & J. Alcalá, 2008. "A bootstrap approach to model checking for linear models under length-biased data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(3), pages 519-543, September.
    13. Biedermann, Stefanie & Dette, Holger, 2001. "Optimal designs for testing the functional form of a regression via nonparametric estimation techniques," Statistics & Probability Letters, Elsevier, vol. 52(2), pages 215-224, April.

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