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Estimation and Inference in Semi-Functional Partially Linear Measurement Error Models

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Abstract

This article studies the estimation and statistical inference problems of semi-functional partially linear regression models when the covariates in the linear part are measured with additive error. To obtain the estimation of the parametric component, a corrected profile least-squares based estimation procedure is developed. Asymptotic properties of the proposed estimators are established under some mild assumptions. To test hypothesis on the parametric part, the authors 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 a weighted sum of independent standard χ21 . Finally, the authors illustrate the finite sample performance of the methods with some simulation studies and a real data application.

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Author information

Authors and Affiliations

  1. School of Statistics, East China Normal University, Shanghai, 200241, China

    Hanbing Zhu & Riquan Zhang

  2. Department of Biostatistics and Data Science, School of Public Health, the University of Texas Health Science Center at Houston, Houston, 77030, USA

    Gen Zhu

Authors
  1. Hanbing Zhu
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  2. Riquan Zhang
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  3. Gen Zhu
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Corresponding author

Correspondence to Riquan Zhang.

Additional information

This research was supported by National Natural Science Foundation of China under Grant Nos. 11571112, 11501372, 11571148, 11471160, Program of Shanghai Subject Chief Scientist (14XD1401600), the 111 Project of China (B14019), Project of National Social Science Fund of China (15BTJ027) and Research Innovation Program for ECNU Graduates (ykc17083).

This paper was recommended for publication by Editor SUN Liuquan.

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Zhu, H., Zhang, R. & Zhu, G. Estimation and Inference in Semi-Functional Partially Linear Measurement Error Models. J Syst Sci Complex 33, 1179–1199 (2020). https://doi.org/10.1007/s11424-019-8045-z

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  • DOI: https://doi.org/10.1007/s11424-019-8045-z

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