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Empirical likelihood for partial linear models with fixed designs

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  • Wang, Qi-Hua
  • Jing, Bing-Yi

Abstract

The empirical likelihood method of Owen [Owen, A., 1988. Empirical likelihood ratio confidence intervals for single functional. Biometrika 75, 237-249], is extended to partial linear models with fixed designs in this paper. A nonparametric version of Wilks' theorem is derived. The result is then used to construct confidence regions of the parameter vector in the partial linear models with asymptotically correct coverage probabilities.

Suggested Citation

  • Wang, Qi-Hua & Jing, Bing-Yi, 1999. "Empirical likelihood for partial linear models with fixed designs," Statistics & Probability Letters, Elsevier, vol. 41(4), pages 425-433, February.
    • Handle: RePEc:eee:stapro:v:41:y:1999:i:4:p:425-433
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    References listed on IDEAS

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    1. Chen, S. X., 1994. "Empirical Likelihood Confidence Intervals for Linear Regression Coefficients," Journal of Multivariate Analysis, Elsevier, vol. 49(1), pages 24-40, April.
    2. Song Chen, 1993. "On the accuracy of empirical likelihood confidence regions for linear regression model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(4), pages 621-637, December.
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    Cited by:

    1. 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.
    2. Ruidong Han & Xinghui Wang & Shuhe Hu, 2018. "Asymptotics of the weighted least squares estimation for AR(1) processes with applications to confidence intervals," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(3), pages 479-490, August.
    3. 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.
    4. Yongli Sang, 2021. "A Jackknife Empirical Likelihood Approach for Testing the Homogeneity of K Variances," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(7), pages 1025-1048, October.
    5. Wong, Heung & Liu, Feng & Chen, Min & Ip, Wai Cheung, 2009. "Empirical likelihood based diagnostics for heteroscedasticity in partial linear models," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3466-3477, July.
    6. Qin, Guoyou & Bai, Yang & Zhu, Zhongyi, 2012. "Robust empirical likelihood inference for generalized partial linear models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 32-44.
    7. Zhao, Yichuan & Chen, Feiming, 2008. "Empirical likelihood inference for censored median regression model via nonparametric kernel estimation," Journal of Multivariate Analysis, Elsevier, vol. 99(2), pages 215-231, February.
    8. 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.
    9. 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.
    10. Chen, Xia & Cui, Hengjian, 2008. "Empirical likelihood inference for partial linear models under martingale difference sequence," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2895-2901, December.
    11. Yichuan Zhao & Song Yang, 2008. "Empirical likelihood inference for censored median regression with weighted empirical hazard functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(2), pages 441-457, June.
    12. Wang, Qihua & Wang, Jane-Ling, 2001. "Inference for the Mean Difference in the Two-Sample Random Censorship Model," Journal of Multivariate Analysis, Elsevier, vol. 79(2), pages 295-315, November.
    13. He, Bang-Qiang & Hong, Xing-Jian & Fan, Guo-Liang, 2017. "Block empirical likelihood for partially linear panel data models with fixed effects," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 128-138.
    14. Yongsong Qin & Jianjun Li, 2011. "Empirical likelihood for partially linear models with missing responses at random," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 497-511.
    15. Qi-Hua Wang, 2009. "Statistical estimation in partial linear models with covariate data missing at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(1), pages 47-84, March.
    16. Wang, Qi-Hua & Li, Gang, 2002. "Empirical Likelihood Semiparametric Regression Analysis under Random Censorship," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 469-486, November.

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