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Efficient estimation of quasi-likelihood models using B-splines

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  • Minggen Lu

    (University of Nevada)

Abstract

We consider a simple yet flexible spline estimation method for quasi-likelihood models. We approximate the unknown function by B-splines and apply the Fisher scoring algorithm to compute the estimates. The spline estimate of the nonparametric component achieves the optimal rate of convergence under the smooth condition, and the estimate of the parametric part is shown to be asymptotically normal even if the variance function is misspecified. The semiparametric efficiency of the model can be established if the variance function is correctly specified. A direct and consistent variance estimation method based on the least-squares estimation is proposed. A simulation study is performed to evaluate the numerical performance of the spline estimate. The methodology is illustrated on a crab study.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:69:y:2017:i:5:d:10.1007_s10463-016-0575-8
    DOI: 10.1007/s10463-016-0575-8
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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 & 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.
    3. Jianhua Z. Huang & Liangyue Zhang & Lan Zhou, 2007. "Efficient Estimation in Marginal Partially Linear Models for Longitudinal/Clustered Data Using Splines," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(3), pages 451-477, September.
    4. 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.
    5. J. Fan & J. Chen, 1999. "One‐step local quasi‐likelihood estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 927-943.
    6. 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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