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Testing the linearity in partially linear models

Author

Listed:
  • Na Li
  • Xingzhong Xu
  • Pei Jin

Abstract

A test is proposed to check the linearity of the nonparametric portion in the partially linear regression model with a linear interpolation. The test is given by a p-value which is derived using the fiducial method. This p-value can also be thought as a generalised p-value. Under the null hypothesis, the p-value is uniformly distributed on interval (0, 1). Meanwhile the test is consistent under mild conditions. Finally, a good finite sample performance of the test is investigated by simulations, in which comparisons with other tests are also given.

Suggested Citation

  • Na Li & Xingzhong Xu & Pei Jin, 2011. "Testing the linearity in partially linear models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(1), pages 99-114.
    • Handle: RePEc:taf:gnstxx:v:23:y:2011:i:1:p:99-114
    DOI: 10.1080/10485251003615574
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    References listed on IDEAS

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    1. Gerda Claeskens, 2004. "Restricted likelihood ratio lack‐of‐fit tests using mixed spline models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 909-926, November.
    2. Dennis Cox & Eunmee Koh, 1989. "A smoothing spline based test of model adequacy in polynomial regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(2), pages 383-400, June.
    3. Richard Blundell & Alan Duncan & Krishna Pendakur, 1998. "Semiparametric estimation and consumer demand," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(5), pages 435-461.
    4. Gourieroux, Christian & Holly, Alberto & Monfort, Alain, 1982. "Likelihood Ratio Test, Wald Test, and Kuhn-Tucker Test in Linear Models with Inequality Constraints on the Regression Parameters," Econometrica, Econometric Society, vol. 50(1), pages 63-80, January.
    5. Mary C. Meyer, 2003. "A test for linear versus convex regression function using shape-restricted regression," Biometrika, Biometrika Trust, vol. 90(1), pages 223-232, March.
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    Cited by:

    1. Jeremy E. Reynolds, 2014. "Prevailing Preferences," ILR Review, Cornell University, ILR School, vol. 67(3), pages 1017-1041, July.
    2. Wangli Xu & Xu Guo, 2013. "Checking the adequacy of partial linear models with missing covariates at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(3), pages 473-490, June.
    3. Ravenscroft, Sue & Williams, Paul F., 2021. "Sustaining discreditable accounting research through ignorance: The mainstream elite’s response to the 2008 financial crisis," Accounting, Organizations and Society, Elsevier, vol. 95(C).
    4. Wangli Xu & Xu Guo & Lixing Zhu, 2012. "Goodness-of-fitting for partial linear model with missing response at random," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(1), pages 103-118.

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