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Spline estimation of generalised monotonic regression

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  • Minggen Lu

Abstract

We develop a simple and practical, yet flexible spline estimation method for semiparametric generalised linear models with monotonicity constraints. We propose to approximate the unknown monotone function by monotone B -splines, and employ generalised Rosen algorithm to compute the estimates. We show that the spline estimate of the nonparametric component achieves the optimal rate of convergence under the smooth condition, and that the estimates of regression parameters are asymptotically normal and efficient. The spline-based semiparametric likelihood ratio test (LRT) is also established. Moreover, a direct variance estimation method based on least-squares estimation is proposed. The finite sample performance of the spline estimates is evaluated by a Monte Carlo study. The methodology is illustrated on an air pollution study.

Suggested Citation

  • Minggen Lu, 2015. "Spline estimation of generalised monotonic regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(1), pages 19-39, March.
    • Handle: RePEc:taf:gnstxx:v:27:y:2015:i:1:p:19-39
    DOI: 10.1080/10485252.2014.972953
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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. 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.
    4. Jamshidian, Mortaza, 2004. "On algorithms for restricted maximum likelihood estimation," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 137-157, March.
    5. 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.
    6. Hazelton, Martin L. & Turlach, Berwin A., 2011. "Semiparametric regression with shape-constrained penalized splines," Computational Statistics & Data Analysis, Elsevier, vol. 55(10), pages 2871-2879, October.
    7. Ying Zhang & Lei Hua & Jian Huang, 2010. "A Spline‐Based Semiparametric Maximum Likelihood Estimation Method for the Cox Model with Interval‐Censored Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 338-354, June.
    8. Mary Meyer & Amber Hackstadt & Jennifer Hoeting, 2011. "Bayesian estimation and inference for generalised partial linear models using shape-restricted splines," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(4), pages 867-884.
    9. Lu, Minggen, 2010. "Spline-based sieve maximum likelihood estimation in the partly linear model under monotonicity constraints," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2528-2542, November.
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    2. 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.
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    4. 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.

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