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Jackknife empirical likelihood of error variance in partially linear varying-coefficient errors-in-variables models

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  • Ai-Ai Liu

    (Tongji University)

  • Han-Ying Liang

    (Tongji University)

Abstract

For the partially linear varying-coefficient model when the parametric covariates are measured with additive errors, the estimator of the error variance is defined based on residuals of the model. At the same time, we construct Jackknife estimator as well as Jackknife empirical likelihood statistic of the error variance. Under both the response variables and their associated covariates form a stationary $$\alpha $$ α -mixing sequence, we prove that the proposed estimators and Jackknife empirical likelihood statistic are asymptotic normality and asymptotic $$\chi ^2$$ χ 2 distribution, respectively. Numerical simulations are carried out to assess the performance of the proposed method.

Suggested Citation

  • Ai-Ai Liu & Han-Ying Liang, 2017. "Jackknife empirical likelihood of error variance in partially linear varying-coefficient errors-in-variables models," Statistical Papers, Springer, vol. 58(1), pages 95-122, March.
    • Handle: RePEc:spr:stpapr:v:58:y:2017:i:1:d:10.1007_s00362-015-0689-8
    DOI: 10.1007/s00362-015-0689-8
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    References listed on IDEAS

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    1. Yu Miao & Fangfang Zhao & Ke Wang & Yanping Chen, 2013. "Asymptotic normality and strong consistency of LS estimators in the EV regression model with NA errors," Statistical Papers, Springer, vol. 54(1), pages 193-206, February.
    2. Jing, Bing-Yi & Yuan, Junqing & Zhou, Wang, 2009. "Jackknife Empirical Likelihood," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1224-1232.
    3. Xuemin Zi & Changliang Zou & Yukun Liu, 2012. "Two-sample empirical likelihood method for difference between coefficients in linear regression model," Statistical Papers, Springer, vol. 53(1), pages 83-93, February.
    4. Liang Peng & Yongcheng Qi & Ingrid Van Keilegom, 2012. "Jackknife empirical likelihood method for copulas," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 74-92, March.
    5. Gong, Yun & Peng, Liang & Qi, Yongcheng, 2010. "Smoothed jackknife empirical likelihood method for ROC curve," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1520-1531, July.
    6. Guo-Liang Fan & Han-Ying Liang & Jiang-Feng Wang, 2013. "Empirical likelihood for heteroscedastic partially linear errors-in-variables model with α-mixing errors," Statistical Papers, Springer, vol. 54(1), pages 85-112, February.
    7. Liang Peng & Yongcheng Qi, 2010. "Smoothed jackknife empirical likelihood method for tail copulas," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 514-536, November.
    8. Sukhbir Singh & Kanchan Jain & Suresh Sharma, 2014. "Replicated measurement error model under exact linear restrictions," Statistical Papers, Springer, vol. 55(2), pages 253-274, May.
    9. Peng, Liang & Qi, Yongcheng & Van Keilegom, Ingrid, 2012. "Jackknife empirical likelihood method for copulas," LIDAM Reprints ISBA 2012013, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Feng, Huijun & Peng, Liang, 2012. "Jackknife empirical likelihood tests for error distributions in regression models," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 63-75.
    11. Shao, Qi-Man, 1993. "Complete convergence for [alpha]-mixing sequences," Statistics & Probability Letters, Elsevier, vol. 16(4), pages 279-287, March.
    12. 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.
    13. Xiuli Wang & Gaorong Li & Lu Lin, 2011. "Empirical likelihood inference for semi-parametric varying-coefficient partially linear EV models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(2), pages 171-185, March.
    14. Francesco Bravo, 2014. "Varying coefficients partially linear models with randomly censored data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 383-412, April.
    15. Huang, Zhensheng & Zhang, Riquan, 2009. "Empirical likelihood for nonparametric parts in semiparametric varying-coefficient partially linear models," Statistics & Probability Letters, Elsevier, vol. 79(16), pages 1798-1808, August.
    16. 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.
    17. Chuanhua Wei & Yubo Luo & Xizhi Wu, 2012. "Empirical likelihood for partially linear additive errors-in-variables models," Statistical Papers, Springer, vol. 53(2), pages 485-496, May.
    18. You, Jinhong & Zhou, Yong, 2006. "Empirical likelihood for semiparametric varying-coefficient partially linear regression models," Statistics & Probability Letters, Elsevier, vol. 76(4), pages 412-422, February.
    19. You, Jinhong & Zhou, Xian & Chen, Gemai, 2005. "Jackknifing in partially linear regression models with serially correlated errors," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 386-404, February.
    20. Sanying Feng & Liugen Xue, 2014. "Bias-corrected statistical inference for partially linear varying coefficient errors-in-variables models with restricted condition," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(1), pages 121-140, February.
    21. Liebscher E., 2001. "Estimation Of The Density And The Regression Function Under Mixing Conditions," Statistics & Risk Modeling, De Gruyter, vol. 19(1), pages 9-26, January.
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    Cited by:

    1. Yongcheng Qi, 2018. "Jackknife Empirical Likelihood Methods," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 7(2), pages 20-22, June.

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