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A flexible approach to inference in semiparametric regression models with correlated errors using Gaussian processes

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  • He, Heping
  • Severini, Thomas A.

Abstract

Consider a semiparametric regression model in which the mean function depends on a finite-dimensional regression parameter as the parameter of interest and an unknown function as a nuisance parameter. A method of inference in such models is proposed, using a type of integrated likelihood in which the unknown function is eliminated by averaging with respect to a given distribution, which we take to be a Gaussian process with a covariance function chosen to reflect the assumptions about the function. This approach is easily implemented and can be applied to a wide range of models using the same basic methodology. The consistency and asymptotic normality of the estimator of the parameter of interest are established under mild conditions. The proposed method is illustrated on several examples.

Suggested Citation

  • He, Heping & Severini, Thomas A., 2016. "A flexible approach to inference in semiparametric regression models with correlated errors using Gaussian processes," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 316-329.
    • Handle: RePEc:eee:csdana:v:103:y:2016:i:c:p:316-329
    DOI: 10.1016/j.csda.2016.05.010
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    References listed on IDEAS

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    1. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, January.
    2. Thomas A. Severini, 2007. "Integrated likelihood functions for non-Bayesian inference," Biometrika, Biometrika Trust, vol. 94(3), pages 529-542.
    3. H. He & T. Severini, 2014. "Integrated likelihood inference in semiparametric regression models," METRON, Springer;Sapienza Università di Roma, vol. 72(2), pages 185-199, August.
    4. Choi, Taeryon & Lee, Jaeyong & Roy, Anindya, 2009. "A note on the Bayes factor in a semiparametric regression model," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1316-1327, July.
    5. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, January.
    6. Weixin Yao & Runze Li, 2013. "New local estimation procedure for a non-parametric regression function for longitudinal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(1), pages 123-138, January.
    7. Inyoung Kim & Noah D. Cohen & Raymond J. Carroll, 2003. "Semiparametric Regression Splines in Matched Case-Control Studies," Biometrics, The International Biometric Society, vol. 59(4), pages 1158-1169, December.
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    Cited by:

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    2. Sandra De Iaco & Donato Posa & Claudia Cappello & Sabrina Maggio, 2021. "On Some Characteristics of Gaussian Covariance Functions," International Statistical Review, International Statistical Institute, vol. 89(1), pages 36-53, April.

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