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

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  • Chuanhua Wei
  • Qihua Wang

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

Suggested Citation

  • Chuanhua Wei & Qihua Wang, 2012. "Statistical inference on restricted partially linear additive errors-in-variables models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 757-774, December.
  • Handle: RePEc:spr:testjl:v:21:y:2012:i:4:p:757-774
    DOI: 10.1007/s11749-011-0279-6
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Jun Zhang & Junpeng Zhu & Yan Zhou & Xia Cui & Tao Lu, 2020. "Multiplicative regression models with distortion measurement errors," Statistical Papers, Springer, vol. 61(5), pages 2031-2057, October.
    2. Fan, Guo-Liang & Liang, Han-Ying & Shen, Yu, 2016. "Penalized empirical likelihood for high-dimensional partially linear varying coefficient model with measurement errors," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 183-201.
    3. Jun Zhang & Junpeng Zhu & Zhenghui Feng, 2019. "Estimation and hypothesis test for single-index multiplicative models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 242-268, March.
    4. Zhang, Jun & Feng, Zhenghui & Peng, Heng, 2018. "Estimation and hypothesis test for partial linear multiplicative models," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 87-103.
    5. Jun Zhang & Xia Cui & Heng Peng, 2020. "Estimation and hypothesis test for partial linear single-index multiplicative models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 699-740, June.
    6. Jun Zhang & Nanguang Zhou & Zipeng Sun & Gaorong Li & Zhenghong Wei, 2016. "Statistical inference on restricted partial linear regression models with partial distortion measurement errors," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(4), pages 304-331, November.
    7. Chuanhua Wei & Jin Yang, 2020. "Stochastic restricted estimation in partially linear additive errors-in-variables models," Statistical Papers, Springer, vol. 61(3), pages 1269-1279, June.
    8. Jianhong Shi & Fanrong Zhao, 2018. "Statistical inference for heteroscedastic semi-varying coefficient EV models under restricted condition," Statistical Papers, Springer, vol. 59(2), pages 487-511, June.
    9. Yang, Jing & Yang, Hu, 2016. "A robust penalized estimation for identification in semiparametric additive models," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 268-277.
    10. Zhangong Zhou & Linjun Tang, 2019. "Testing for parametric component of partially linear models with missing covariates," Statistical Papers, Springer, vol. 60(3), pages 747-760, June.
    11. Jun Zhang, 2021. "Estimation and variable selection for partial linear single-index distortion measurement errors models," Statistical Papers, Springer, vol. 62(2), pages 887-913, April.
    12. 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.

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