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Statistical inference for heteroscedastic semi-varying coefficient EV models under restricted condition

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  • Jianhong Shi

    (Shanxi Normal University)

  • Fanrong Zhao

    (Shanxi Normal University)

Abstract

This paper studies the estimation and testing problems for a class of heteroscedastic semi-varying coefficient errors-in-variables models under additional restricted condition. Initial restricted estimates for the regression coefficients and varying coefficients are first constructed based on the profile least squares procedure without considering the heteroscedasticity, then a bias-corrected kernel type restricted estimate for the variance function is proposed, which in turn is used to construct re-weighted bias-corrected restricted estimates of the regression coefficients and the varying coefficients. The large sample properties including the consistency and asymptotic normality are thoroughly investigated. To test hypotheses on the parametric component, we propose a test statistic based on the profile Lagrange multiplier, and show that its asymptotic null distribution is standard chi-squared distribution. Some simulation studies are conducted to evaluate the finite sample performance of the proposed methods.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:59:y:2018:i:2:d:10.1007_s00362-016-0773-8
    DOI: 10.1007/s00362-016-0773-8
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    References listed on IDEAS

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    1. You, Jinhong & Zhou, Xian & Zhou, Yong, 2010. "Statistical inference for panel data semiparametric partially linear regression models with heteroscedastic errors," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1079-1101, May.
    2. Shen, Si-Lian & Cui, Jian-Ling & Mei, Chang-Lin & Wang, Chun-Wei, 2014. "Estimation and inference of semi-varying coefficient models with heteroscedastic errors," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 70-93.
    3. 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.
    4. You, Jinhong & Chen, Gemai & Zhou, Yong, 2007. "Statistical inference of partially linear regression models with heteroscedastic errors," Journal of Multivariate Analysis, Elsevier, vol. 98(8), pages 1539-1557, September.
    5. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    6. Hu, Xuemei & Wang, Zhizhong & Zhao, Zhiwei, 2009. "Empirical likelihood for semiparametric varying-coefficient partially linear errors-in-variables models," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1044-1052, April.
    7. Zhang, Weiwei & Li, Gaorong & Xue, Liugen, 2011. "Profile inference on partially linear varying-coefficient errors-in-variables models under restricted condition," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 3027-3040, November.
    8. 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.
    9. Hua Liang & Suojin Wang & Raymond J. Carroll, 2007. "Partially linear models with missing response variables and error-prone covariates," Biometrika, Biometrika Trust, vol. 94(1), pages 185-198.
    10. Haibo Zhou & Jinhong You & Bin Zhou, 2010. "Statistical inference for fixed-effects partially linear regression models with errors in variables," Statistical Papers, Springer, vol. 51(3), pages 629-650, September.
    11. Hengjian Cui & Efang Kong, 2006. "Empirical Likelihood Confidence Region for Parameters in Semi‐linear Errors‐in‐Variables Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(1), pages 153-168, March.
    12. 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.
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