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Integrated likelihood inference in semiparametric regression models

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  • H. He
  • T. Severini

Abstract

Consider a linear semiparametric regression model with normal errors in which the mean function depends on two parameters, a p-dimensional regression parameter, which is the parameter of interest, and an unknown function, which is a nuisance parameter. We consider estimation of the parameter of interest using an integrated likelihood function, in which the nuisance parameter is eliminated from the likelihood function by averaging with respect to some distribution. Here we take this distribution to be a Gaussian process with a given covariance function, which may depend on additional parameters. Likelihood inference based on the resulting integrated likelihood is considered and the properties of the score statistic based on the integrated likelihood, the maximum integrated likelihood estimator, and the integrated likelihood ratio statistic are presented. The methodology is illustrated on two examples. Copyright Sapienza Università di Roma 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metron:v:72:y:2014:i:2:p:185-199
    DOI: 10.1007/s40300-014-0042-3
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    References listed on IDEAS

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    1. Thomas A. Severini, 2007. "Integrated likelihood functions for non-Bayesian inference," Biometrika, Biometrika Trust, vol. 94(3), pages 529-542.
    2. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, October.
    3. Simon N. Wood, 2011. "Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 3-36, January.
    4. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, October.
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    1. H. V. Kulkarni & S. M. Patil, 2021. "Uniformly implementable small sample integrated likelihood ratio test for one-way and two-way ANOVA under heteroscedasticity and normality," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(2), pages 273-305, June.
    2. 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.

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