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Root-n consistent estimation in partly linear regression models

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  • Schick, Anton

Abstract

This paper deals with root-n consistent estimation of the parameter [beta] in the partly linear regression model Y = [beta]T U + [gamma](X) + [var epsilon], where , [gamma] is a function on [0, 1]q, the error variable [var epsilon] satisfies E([var epsilon] / U, X) = 0 and E([var epsilon]2 / U, X) is bounded, and the random vector (UT, XT)T is . Under an identifiability condition, least squares type estimates of [beta] are shown to be root-n consistent under mild smoothness assumptions on [gamma], h or both, where h(X) = E(U X). No assumption on the distribution of X are imposed. This result improves on a result of Chen (1988).

Suggested Citation

  • Schick, Anton, 1996. "Root-n consistent estimation in partly linear regression models," Statistics & Probability Letters, Elsevier, vol. 28(4), pages 353-358, August.
    • Handle: RePEc:eee:stapro:v:28:y:1996:i:4:p:353-358
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    References listed on IDEAS

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    1. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    2. Rice, John, 1986. "Convergence rates for partially splined models," Statistics & Probability Letters, Elsevier, vol. 4(4), pages 203-208, June.
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    Cited by:

    1. Liang, Hua & Härdle, Wolfgang, 1997. "Large sample theory of the estimation of the error distribution for a semiparametric model," SFB 373 Discussion Papers 1997,101, 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.
    3. Aneiros-Pérez, Germán & Vieu, Philippe, 2006. "Semi-functional partial linear regression," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1102-1110, June.
    4. Müller, Ursula U. & Schick, Anton & Wefelmeyer, Wolfgang, 2014. "Testing for additivity in partially linear regression with possibly missing responses," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 51-61.
    5. Cui, Xia & Lu, Ying & Peng, Heng, 2017. "Estimation of partially linear regression models under the partial consistency property," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 103-121.
    6. Müller Ursula U. & Schick Anton & Wefelmeyer Wolfgang, 2007. "Estimating the error distribution function in semiparametric regression," Statistics & Risk Modeling, De Gruyter, vol. 25(1), pages 1-18, January.
    7. Michael Levine, 2019. "Robust functional estimation in the multivariate partial linear model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(4), pages 743-770, August.

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