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Statistical inference on restricted partially linear additive errors-in-variables models

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  • Chuanhua Wei

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  • Qihua Wang
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    Abstract

    As a useful extension of partially linear models and additive models, partially linear additive model has been paid considerable attention in recent years. This paper considers statistical inference for the semiparametric model when the covariates in the linear part are measured with additive error. To test hypothesis on the parametric component, we propose a novel test statistic based on the difference between the corrected residual sums of squares under the null and alternative hypotheses, and show that its limiting distribution is that of a weighted sum of independent standard $\chi_{1}^{2}$ . We also develop an adjusted test statistic, which has an asymptotically standard chi-squared distribution. Some simulation studies are conducted to illustrate our approaches. Copyright Sociedad de Estadística e Investigación Operativa 2012

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    File URL: http://hdl.handle.net/10.1007/s11749-011-0279-6
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    Bibliographic Info

    Article provided by Springer in its journal TEST.

    Volume (Year): 21 (2012)
    Issue (Month): 4 (December)
    Pages: 757-774

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    Handle: RePEc:spr:testjl:v:21:y:2012:i:4:p:757-774

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    Related research

    Keywords: Errors-in-variables; Partially linear additive model; Corrected-profile least-squares approach; Restricted estimator; 62G05; 62G10;

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    1. Opsomer, Jean D., 2000. "Asymptotic Properties of Backfitting Estimators," Journal of Multivariate Analysis, Elsevier, vol. 73(2), pages 166-179, May.
    2. Wang, Qihua, 1999. "Estimation of Partial Linear Error-in-Variables Models with Validation Data," Journal of Multivariate Analysis, Elsevier, vol. 69(1), pages 30-64, April.
    3. Manzan, Sebastiano & Zerom, Dawit, 2005. "Kernel estimation of a partially linear additive model," Statistics & Probability Letters, Elsevier, vol. 72(4), pages 313-322, May.
    4. Qihua Wang, 2002. "Empirical likelihood-based inference in linear errors-in-covariables models with validation data," Biometrika, Biometrika Trust, vol. 89(2), pages 345-358, June.
    5. You, Jinhong & Chen, Gemai, 2006. "Estimation of a semiparametric varying-coefficient partially linear errors-in-variables model," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 324-341, February.
    6. Przystalski, Marcin & Krajewski, Pawel, 2007. "Constrained estimators of treatment parameters in semiparametric models," Statistics & Probability Letters, Elsevier, vol. 77(9), pages 914-919, May.
    7. Shalabh & Garg, Gaurav & Misra, Neeraj, 2007. "Restricted regression estimation in measurement error models," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 1149-1166, October.
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