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Polynomial Spline Estimation for a Generalized Additive Coefficient Model

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  • LAN XUE
  • HUA LIANG

Abstract

We study a semiparametric generalized additive coefficient model (GACM), in which linear predictors in the conventional generalized linear models are generalized to unknown functions depending on certain covariates, and approximate the non-parametric functions by using polynomial spline. The asymptotic expansion with optimal rates of convergence for the estimators of the non-parametric part is established. Semiparametric generalized likelihood ratio test is also proposed to check if a non-parametric coefficient can be simplified as a parametric one. A conditional bootstrap version is suggested to approximate the distribution of the test under the null hypothesis. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed methods. We further apply the proposed model and methods to a data set from a human visceral Leishmaniasis study conducted in Brazil from 1994 to 1997. Numerical results outperform the traditional generalized linear model and the proposed GACM is preferable. Copyright (c) 2009 Board of the Foundation of the Scandinavian Journal of Statistics.

Suggested Citation

  • Lan Xue & Hua Liang, 2010. "Polynomial Spline Estimation for a Generalized Additive Coefficient Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(1), pages 26-46.
  • Handle: RePEc:bla:scjsta:v:37:y:2010:i:1:p:26-46
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    File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9469.2009.00655.x
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    References listed on IDEAS

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    1. Huang, Jianhua Z., 1998. "Functional ANOVA Models for Generalized Regression," Journal of Multivariate Analysis, Elsevier, vol. 67(1), pages 49-71, October.
    2. Jianhua Z. Huang, 2002. "Varying-coefficient models and basis function approximations for the analysis of repeated measurements," Biometrika, Biometrika Trust, vol. 89(1), pages 111-128, March.
    3. Jianhua Z. Huang & Linxu Liu, 2006. "Polynomial Spline Estimation and Inference of Proportional Hazards Regression Models with Flexible Relative Risk Form," Biometrics, The International Biometric Society, vol. 62(3), pages 793-802, September.
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    Cited by:

    1. repec:spr:aistmt:v:69:y:2017:i:5:d:10.1007_s10463-016-0575-8 is not listed on IDEAS
    2. Shujie Ma & Peter X.-K. Song, 2015. "Varying Index Coefficient Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 341-356, March.
    3. Zhiguo Li & Kouros Owzar, 2016. "Fitting Cox Models with Doubly Censored Data Using Spline-Based Sieve Marginal Likelihood," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 476-486, June.
    4. repec:spr:metrik:v:81:y:2018:i:1:d:10.1007_s00184-017-0631-2 is not listed on IDEAS
    5. 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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