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Simultaneous confidence band and hypothesis test in generalised varying-coefficient models

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  • Zhang, Wenyang
  • Peng, Heng

Abstract

Generalised varying-coefficient models (GVC) are very important models. There are a considerable number of literature addressing these models. However, most of the existing literature are devoted to the estimation procedure. In this paper, we systematically investigate the statistical inference for GVC, which includes confidence band as well as hypothesis test. We establish the asymptotic distribution of the maximum discrepancy between the estimated functional coefficient and the true functional coefficient. We compare different approaches for the construction of confidence band and hypothesis test. Finally, the proposed statistical inference methods are used to analyse the data from China about contraceptive use there, which leads to some interesting findings.

Suggested Citation

  • Zhang, Wenyang & Peng, Heng, 2010. "Simultaneous confidence band and hypothesis test in generalised varying-coefficient models," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1656-1680, August.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:7:p:1656-1680
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    References listed on IDEAS

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    1. Jianqing Fan, 2004. "Generalised likelihood ratio tests for spectral density," Biometrika, Biometrika Trust, vol. 91(1), pages 195-209, March.
    2. Jianqing Fan & Wenyang Zhang, 2000. "Simultaneous Confidence Bands and Hypothesis Testing in Varying‐coefficient Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 715-731, December.
    3. Jiancheng Jiang & Zhou Haibo, 2007. "Additive hazard regression with auxiliary covariates," Biometrika, Biometrika Trust, vol. 94(2), pages 359-369.
    4. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
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    Cited by:

    1. Philipp Bach & Sven Klaassen & Jannis Kueck & Martin Spindler, 2020. "Uniform Inference in High-Dimensional Generalized Additive Models," Papers 2004.01623, arXiv.org.
    2. Yang, Suigen & Xue, Liugen & Li, Gaorong, 2014. "Simultaneous confidence band for single-index random effects models with longitudinal data," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 6-14.
    3. Xia, Xiaochao & Yang, Hu & Li, Jialiang, 2016. "Feature screening for generalized varying coefficient models with application to dichotomous responses," Computational Statistics & Data Analysis, Elsevier, vol. 102(C), pages 85-97.
    4. Zhang, Wenyang & Li, Degui & Xia, Yingcun, 2015. "Estimation in generalised varying-coefficient models with unspecified link functions," Journal of Econometrics, Elsevier, vol. 187(1), pages 238-255.
    5. Xiangjin B. Chen & Jiti Gao & Degui Li & Param Silvapulle, 2018. "Nonparametric Estimation and Forecasting for Time-Varying Coefficient Realized Volatility Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 88-100, January.
    6. Byeong U. Park & Enno Mammen & Young K. Lee & Eun Ryung Lee, 2015. "Varying Coefficient Regression Models: A Review and New Developments," International Statistical Review, International Statistical Institute, vol. 83(1), pages 36-64, April.

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