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Asymptotic Distributions For Two Estimators Of The Single-Index Model

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  • Xia, Yingcun
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    Abstract

    The single-index model is one of the most popular semiparametric models in applied quantitative sciences. Two new estimation methods have been proposed recently by Hristache, Juditski, and Spokoiny (2001, Annals of Statistics 29, 595 623) and Xia, Tong, Li, and Zhu (2002, Journal of the Royal Statistical Society, Series B 64, 363 410), respectively. However, their asymptotic distributions have not been investigated yet. In this paper, alternative versions for the methods are investigated. Asymptotic distributions of the estimators are derived. Efficiency comparisons between the estimation methods are made.The author is most grateful to Professor O. Linton and Professor W. H rdle for helpful discussions. Valuable comments from two anonymous reviewers have improved the presentation of the paper substantially. The research has been partially supported by NUS research grant R-155-000-048-112, National University of Singapore, Singapore, and the Alexander von Humboldt Foundation, Germany.

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    Bibliographic Info

    Article provided by Cambridge University Press in its journal Econometric Theory.

    Volume (Year): 22 (2006)
    Issue (Month): 06 (December)
    Pages: 1112-1137

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    Handle: RePEc:cup:etheor:v:22:y:2006:i:06:p:1112-1137_06

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    Cited by:
    1. Jia Chen & Jiti Gao & Degui Li, 2010. "Estimation in Single-Index Panel Data Models with Heterogeneous Link Functions," School of Economics Working Papers 2010-09, University of Adelaide, School of Economics.
    2. Wolfgang Härdle & Oliver Linton & Yingcun Xia, 2009. "Optimal Smoothing for a Computationallyand StatisticallyEfficient Single Index Estimator," STICERD - Econometrics Paper Series /2009/537, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    3. Jia Chen & Jiti Gao & Degui Li, 2011. "Estimation in Partially Linear Single-Index Panel Data Models with Fixed Effects," Monash Econometrics and Business Statistics Working Papers 14/11, Monash University, Department of Econometrics and Business Statistics.
    4. Yi, Grace Y. & He, Wenqing & Liang, Hua, 2009. "Analysis of correlated binary data under partially linear single-index logistic models," Journal of Multivariate Analysis, Elsevier, vol. 100(2), pages 278-290, February.
    5. Huang, Zhensheng & Pang, Zhen & Lin, Bingqing & Shao, Quanxi, 2014. "Model structure selection in single-index-coefficient regression models," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 159-175.
    6. Escanciano, Juan Carlos & Song, Kyungchul, 2010. "Testing single-index restrictions with a focus on average derivatives," Journal of Econometrics, Elsevier, vol. 156(2), pages 377-391, June.
    7. Guo, Xu & Xu, Wangli & Zhu, Lixing, 2014. "Multi-index regression models with missing covariates at random," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 345-363.
    8. Chang, Ziqing & Xue, Liugen & Zhu, Lixing, 2010. "On an asymptotically more efficient estimation of the single-index model," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1898-1901, September.
    9. Lu, Xuewen, 2010. "Asymptotic distributions of two "synthetic data" estimators for censored single-index models," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 999-1015, April.
    10. Pang, Zhen & Xue, Liugen, 2012. "Estimation for the single-index models with random effects," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1837-1853.
    11. Wanrong Liu & Xuewen Lu, 2011. "Empirical likelihood for density-weighted average derivatives," Statistical Papers, Springer, vol. 52(2), pages 391-412, May.
    12. Feng, Long & Zou, Changliang & Wang, Zhaojun, 2012. "Rank-based inference for the single-index model," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 535-541.
    13. Rothe, Christoph, 2009. "Semiparametric estimation of binary response models with endogenous regressors," Journal of Econometrics, Elsevier, vol. 153(1), pages 51-64, November.

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