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Empirical likelihood for heteroscedastic partially linear single-index models with growing dimensional data

Author

Listed:
  • Jianglin Fang

    () (Hunan Institute of Engineering)

  • Wanrong Liu

    (Hunan Normal University)

  • Xuewen Lu

    (University of Calgary)

Abstract

Abstract In this paper, we propose a new approach to the empirical likelihood inference for the parameters in heteroscedastic partially linear single-index models. In the growing dimensional setting, it is proved that estimators based on semiparametric efficient score have the asymptotic consistency, and the limit distribution of the empirical log-likelihood ratio statistic for parameters $$(\beta ^{\top },\theta ^{\top })^{\top }$$ ( β ⊤ , θ ⊤ ) ⊤ is a normal distribution. Furthermore, we show that the empirical log-likelihood ratio based on the subvector of $$\beta $$ β is an asymptotic chi-square random variable, which can be used to construct the confidence interval or region for the subvector of $$\beta $$ β . The proposed method can naturally be applied to deal with pure single-index models and partially linear models with high-dimensional data. The performance of the proposed method is illustrated via a real data application and numerical simulations.

Suggested Citation

  • Jianglin Fang & Wanrong Liu & Xuewen Lu, 2018. "Empirical likelihood for heteroscedastic partially linear single-index models with growing dimensional data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(3), pages 255-281, April.
  • Handle: RePEc:spr:metrik:v:81:y:2018:i:3:d:10.1007_s00184-018-0642-7
    DOI: 10.1007/s00184-018-0642-7
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    References listed on IDEAS

    as
    1. Lixing Zhu & Liugen Xue, 2006. "Empirical likelihood confidence regions in a partially linear single‐index model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 549-570, June.
    2. Shi, Jian & Lau, Tai-Shing, 2000. "Empirical Likelihood for Partially Linear Models," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 132-148, January.
    3. Yingcun Xia & Howell Tong & W. K. Li & Li‐Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410, August.
    4. Song Xi Chen & Liang Peng & Ying-Li Qin, 2009. "Effects of data dimension on empirical likelihood," Biometrika, Biometrika Trust, vol. 96(3), pages 711-722.
    5. Yanyuan Ma & Liping Zhu, 2013. "Doubly robust and efficient estimators for heteroscedastic partially linear single-index models allowing high dimensional covariates," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(2), pages 305-322, March.
    6. Xia, Yingcun & Härdle, Wolfgang, 2006. "Semi-parametric estimation of partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1162-1184, May.
    7. Xue, Liu-Gen & Zhu, Lixing, 2006. "Empirical likelihood for single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1295-1312, July.
    8. Yanyuan Ma & Jeng-Min Chiou & Naisyin Wang, 2006. "Efficient semiparametric estimator for heteroscedastic partially linear models," Biometrika, Biometrika Trust, vol. 93(1), pages 75-84, March.
    9. Lai, Peng & Wang, Qihua, 2014. "Semiparametric efficient estimation for partially linear single-index models with responses missing at random," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 33-50.
    10. Qihua Wang, 2002. "Empirical likelihood-based inference in linear errors-in-covariables models with validation data," Biometrika, Biometrika Trust, vol. 89(2), pages 345-358, June.
    11. Lu, Xuewen, 2009. "Empirical likelihood for heteroscedastic partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 387-396, March.
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