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Local Linear Estimation in Partly Linear Models

Author

Listed:
  • Hamilton, Scott A.
  • Truong, Young K.

Abstract

Let (X, B, Y) denote a random vector such thatBandYare real-valued, andX[set membership, variant]2. Local linear estimates are used in the partial regression method for estimating the regression functionE(Y|X, B)=[alpha]B+m(X), where[alpha]is an unknown parameter, andm(·) is a smooth function. Under appropriate conditions, asymptotic distributions of estimates of[alpha]andm(·) are established. Moreover, it is shown that these estimates achieve the best possible rates of convergence in the indicated semi-parametric problems.

Suggested Citation

  • Hamilton, Scott A. & Truong, Young K., 1997. "Local Linear Estimation in Partly Linear Models," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 1-19, January.
    • Handle: RePEc:eee:jmvana:v:60:y:1997:i:1:p:1-19
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    Citations

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    Cited by:

    1. Qin, Gengsheng & Jing, Bing-Yi, 2001. "Censored Partial Linear Models and Empirical Likelihood," Journal of Multivariate Analysis, Elsevier, vol. 78(1), pages 37-61, July.
    2. Gemai Chen & Jinhong You, 2005. "An asymptotic theory for semiparametric generalized least squares estimation in partially linear regression models," Statistical Papers, Springer, vol. 46(2), pages 173-193, April.
    3. Zhao, Haibing & You, Jinhong, 2011. "Difference based estimation for partially linear regression models with measurement errors," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1321-1338, November.
    4. Yunlu Jiang, 2015. "Robust estimation in partially linear regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(11), pages 2497-2508, November.
    5. Xuejun Wang & Xin Deng & Shuhe Hu, 2018. "On consistency of the weighted least squares estimators in a semiparametric regression model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(7), pages 797-820, October.
    6. 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.
    7. Liang, Han-Ying & Fan, Guo-Liang, 2009. "Berry-Esseen type bounds of estimators in a semiparametric model with linear process errors," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 1-15, January.
    8. Jing-Jing Zhang & Han-Ying Liang & Amei Amei, 2014. "Asymptotic normality of estimators in heteroscedastic errors-in-variables model," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(2), pages 165-195, April.
    9. Xingcai Zhou & Xinsheng Liu & Shuhe Hu, 2010. "Moment consistency of estimators in partially linear models under NA samples," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(3), pages 415-432, November.
    10. Chang, Xiao-Wen & Qu, Leming, 2004. "Wavelet estimation of partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 47(1), pages 31-48, August.
    11. 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.
    12. Qi-Hua Wang & Bing-Yi Jing, 2003. "Empirical likelihood for partial linear models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(3), pages 585-595, September.
    13. You, Jinhong & Sun, Xiaoqian & Pang, Wan-kai & Leung, Ping-kei, 2002. "Jackknifing type weighted least squares estimators in partially linear regression models," Statistics & Probability Letters, Elsevier, vol. 60(1), pages 17-31, November.
    14. Liang, Hua, 2006. "Estimation in partially linear models and numerical comparisons," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 675-687, February.
    15. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    16. You, Jinhong & Chen, Gemai, 2006. "Wild bootstrap estimation in partially linear models with heteroscedasticity," Statistics & Probability Letters, Elsevier, vol. 76(4), pages 340-348, February.
    17. Alexandra Soberon & Irene D’Hers, 2020. "The Environmental Kuznets Curve: A Semiparametric Approach with Cross-Sectional Dependence," JRFM, MDPI, vol. 13(11), pages 1-23, November.
    18. Ibacache-Pulgar, Germán & Paula, Gilberto A., 2011. "Local influence for Student-t partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1462-1478, March.
    19. Zhou, Xian & You, Jinhong, 2004. "Wavelet estimation in varying-coefficient partially linear regression models," Statistics & Probability Letters, Elsevier, vol. 68(1), pages 91-104, June.
    20. Zhou, Xing-cai & Lin, Jin-guan, 2013. "Asymptotic properties of wavelet estimators in semiparametric regression models under dependent errors," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 251-270.
    21. 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.
    22. Lu, Minggen, 2010. "Spline-based sieve maximum likelihood estimation in the partly linear model under monotonicity constraints," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2528-2542, November.

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