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Estimation and hypothesis test on partial linear models with additive distortion measurement errors

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  • Zhang, Jun
  • Zhou, Yan
  • Lin, Bingqing
  • Yu, Yao

Abstract

We consider estimation and hypothesis test for partial linear measurement errors models when the response variable and covariates in the linear part are measured with additive distortion measurement errors, which are unknown functions of a commonly observable confounding variable. We propose a transformation based profile least squares estimator to estimate unknown parameter under unrestricted and restricted conditions. Asymptotic properties for the estimators are established. To test a hypothesis on the parametric components, a test statistic based on the normalized difference between the residual sums of squares under the null and alternative hypotheses is proposed, and we further show that its limiting distribution is a standard chi-squared distribution. Lastly, we suggest a lack-of-fit test of score type for checking the validity of partial linear models. The quadratic form of the scaled test statistic is asymptotically chi-squared under the null hypothesis and a non-centered one under local alternatives converging to the null hypothesis at parametric rates. Simulation studies are conducted to demonstrate the performance of the proposed procedure and a real example is analyzed for an illustration.

Suggested Citation

  • Zhang, Jun & Zhou, Yan & Lin, Bingqing & Yu, Yao, 2017. "Estimation and hypothesis test on partial linear models with additive distortion measurement errors," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 114-128.
    • Handle: RePEc:eee:csdana:v:112:y:2017:i:c:p:114-128
    DOI: 10.1016/j.csda.2017.03.009
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    References listed on IDEAS

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    6. Li, Qi, 2000. "Efficient Estimation of Additive Partially Linear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1073-1092, November.
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    Cited by:

    1. Kangning Wang & Mengjie Hao & Xiaofei Sun, 2021. "Robust and efficient estimating equations for longitudinal data partial linear models and its applications," Statistical Papers, Springer, vol. 62(5), pages 2147-2168, October.

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