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Large sample theory in a semiparametric partially linear errors-in-variables models

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  • Liang, Hua
  • Härdle, Wolfgang
  • Carroll, Raymond J.

Abstract

We consider the partially linear model relating a response Y to predictors (X,T) with mean function XT ß + g (T) when the X's are measured with additive error. The semiparametric likelihood estimate of Severini and Staniswalis (1994) leads to biased estimates of both the parameter ß and the function g(·) when measurement error is ignored. We derive a simple modification of their estimator which is a semiparametric version of the usual parametric correction for attenuation. The resulting estimator of ß is shown to be consistent and its asymptotic distribution theory is derived. Consistent standard error estimates using sandwich-type ideas are also developed.

Suggested Citation

  • Liang, Hua & Härdle, Wolfgang & Carroll, Raymond J., 1997. "Large sample theory in a semiparametric partially linear errors-in-variables models," SFB 373 Discussion Papers 1997,27, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:199727
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    References listed on IDEAS

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    1. Liang, Hua & Härdle, Wolfgang, 1997. "Asymptotic normality of parametric part in partial linear heteroscedastic regression models," SFB 373 Discussion Papers 1997,33, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
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    Cited by:

    1. Weiming Yang & Yiping Yang, 2020. "Composite quantile regression estimation of linear error-in-variable models using instrumental variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(1), pages 1-16, January.
    2. Liang, Hua, 1997. "Asymptotic normality of parametric part in partially linear models with measurement error in the nonparametric part," SFB 373 Discussion Papers 1997,46, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    3. He, Xuming & Liang, Hua, 1997. "Quantile regression estimates for a class of linear and partially linear errors-in-variables models," SFB 373 Discussion Papers 1997,103, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.

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