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Identifiability of single-index models and additive-index models

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  • Wei Lin
  • K. B. Kulasekera

Abstract

We provide a proof for the identifiability for both single-index models and partially linear single-index models assuming only the continuity of the regression function, a condition much weaker than the differentiability conditions assumed in the existing literature. Our discussion is then extended to the identifiability of the additive-index models. Copyright 2007, Oxford University Press.

Suggested Citation

  • Wei Lin & K. B. Kulasekera, 2007. "Identifiability of single-index models and additive-index models," Biometrika, Biometrika Trust, vol. 94(2), pages 496-501.
    • Handle: RePEc:oup:biomet:v:94:y:2007:i:2:p:496-501
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    File URL: http://hdl.handle.net/10.1093/biomet/asm029
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    Cited by:

    1. Jiang, Rong & Qian, Wei-Min & Zhou, Zhan-Gong, 2016. "Weighted composite quantile regression for single-index models," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 34-48.
    2. Lian, Heng & Liang, Hua, 2016. "Separation of linear and index covariates in partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 56-70.
    3. Glen McGee & Ander Wilson & Thomas F. Webster & Brent A. Coull, 2023. "Bayesian multiple index models for environmental mixtures," Biometrics, The International Biometric Society, vol. 79(1), pages 462-474, March.
    4. Jiang, Rong & Qian, Wei-Min, 2016. "Quantile regression for single-index-coefficient regression models," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 305-317.
    5. Lili Yue & Gaorong Li & Heng Lian, 2019. "Identification and estimation in quantile varying-coefficient models with unknown link function," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(4), pages 1251-1275, December.
    6. Hongxia Wang & Zihan Zhao & Hongxia Hao & Chao Huang, 2023. "Estimation and Inference for Spatio-Temporal Single-Index Models," Mathematics, MDPI, vol. 11(20), pages 1-32, October.
    7. Birke, M. & Van Bellegem, S. & Van Keilegom, I., 2014. "Semi-parametric estimation in a single-index model with endogenous variables," LIDAM Discussion Papers ISBA 2014043, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Zijuan Chen & Suojin Wang, 2023. "Inferences for extended partially linear single-index models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 602-622, June.
    9. Jiang, Rong & Zhou, Zhan-Gong & Qian, Wei-Min & Chen, Yong, 2013. "Two step composite quantile regression for single-index models," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 180-191.
    10. Giovanni Forchini & Raoul Theler, 2023. "Semi-parametric modelling of inefficiencies in stochastic frontier analysis," Journal of Productivity Analysis, Springer, vol. 59(2), pages 135-152, April.
    11. Lai, Peng & Li, Gaorong & Lian, Heng, 2013. "Semiparametric estimation of fixed effects panel data single-index model," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1595-1602.
    12. Lin, Wei & Kulasekera, K.B., 2010. "Testing the equality of linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1156-1167, May.
    13. Guo, Xu & Fang, Yun & Zhu, Xuehu & Xu, Wangli & Zhu, Lixing, 2018. "Semiparametric double robust and efficient estimation for mean functionals with response missing at random," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 325-339.
    14. D. Wang & C. S. McMahan & C. M. Gallagher & K. B. Kulasekera, 2014. "Semiparametric group testing regression models," Biometrika, Biometrika Trust, vol. 101(3), pages 587-598.
    15. Hamdy F. F. Mahmoud & Inyoung Kim, 2023. "Semiparametric Integrated and Additive Spatio-Temporal Single-Index Models," Mathematics, MDPI, vol. 11(22), pages 1-15, November.
    16. Jiang, Rong & Yu, Keming, 2020. "Single-index composite quantile regression for massive data," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    17. Rong Jiang & Wei-Min Qian & Zhan-Gong Zhou, 2016. "Single-index composite quantile regression with heteroscedasticity and general error distributions," Statistical Papers, Springer, vol. 57(1), pages 185-203, March.
    18. Hamdy F. F. Mahmoud, 2021. "Parametric Versus Semi and Nonparametric Regression Models," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(2), pages 1-90, March.
    19. Han, Zhong-Cheng & Lin, Jin-Guan & Zhao, Yan-Yong, 2020. "Adaptive semiparametric estimation for single index models with jumps," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).
    20. Chaohua Dong & Jiti Gao & Dag Tjostheim, 2014. "Estimation for Single-index and Partially Linear Single-index Nonstationary Time Series Models," Monash Econometrics and Business Statistics Working Papers 7/14, Monash University, Department of Econometrics and Business Statistics.

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