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Spline-based semiparametric estimation of partially linear Poisson regression with single-index models

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  • Minggen Lu
  • Dana Loomis

Abstract

Epidemiological studies have shown that the high levels of air pollution are associated with the increased mortality. To further characterise the health effects of air pollutants, we propose a spline-based partially linear Poisson single-index model to study the relationship of multi-dimensional air pollution exposure to mortality. B -splines are used to approximate the unknown regression function. A modified Fisher scoring method is applied to simultaneously estimate the linear coefficients and the regression function. The estimator of the regression function is consistent with a better than cubic root convergence rate and the estimators of regression parameters are asymptotically normal and efficient. Also a simple and consistent variance estimation approach based on least-squares method is proposed. An extensive Monte Carlo study is conducted to evaluate the finite sample performance of the proposed spline approach. The method is illustrated using data from an epidemiological study of ambient fine particles.

Suggested Citation

  • Minggen Lu & Dana Loomis, 2013. "Spline-based semiparametric estimation of partially linear Poisson regression with single-index models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(4), pages 905-922, December.
    • Handle: RePEc:taf:gnstxx:v:25:y:2013:i:4:p:905-922
    DOI: 10.1080/10485252.2013.817576
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    References listed on IDEAS

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    1. Lu, Minggen & Zhang, Ying & Huang, Jian, 2009. "Semiparametric Estimation Methods for Panel Count Data Using Monotone B-Splines," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1060-1070.
    2. Minggen Lu & Ying Zhang & Jian Huang, 2007. "Estimation of the mean function with panel count data using monotone polynomial splines," Biometrika, Biometrika Trust, vol. 94(3), pages 705-718.
    3. 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, March.
    4. Delecroix, Michel & Härdle, Wolfgang & Hristache, Marian, 2003. "Efficient estimation in conditional single-index regression," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 213-226, August.
    5. 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. Minggen Lu, 2017. "Efficient estimation of quasi-likelihood models using B-splines," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(5), pages 1099-1127, October.
    2. 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.
    3. Minggen Lu, 2018. "Spline-based quasi-likelihood estimation of mixed Poisson regression with single-index models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(1), pages 1-17, January.
    4. Minggen Lu, 2015. "Spline estimation of generalised monotonic regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(1), pages 19-39, March.

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