彭清艳, 罗金梅, 周建军. 广义部分函数型线性模型的多项式样条估计[J]. 云南大学学报(自然科学版), 2020, 42(6): 1027-1037. doi: 10.7540/j.ynu.20200385
引用本文: 彭清艳, 罗金梅, 周建军. 广义部分函数型线性模型的多项式样条估计[J]. 云南大学学报(自然科学版), 2020, 42(6): 1027-1037. doi: 10.7540/j.ynu.20200385
PENG Qing-yan, LUO Jin-mei, ZHOU Jian-jun. Polynomial spline estimation for generalized partial functional linear regression models[J]. Journal of Yunnan University: Natural Sciences Edition, 2020, 42(6): 1027-1037. DOI: 10.7540/j.ynu.20200385
Citation: PENG Qing-yan, LUO Jin-mei, ZHOU Jian-jun. Polynomial spline estimation for generalized partial functional linear regression models[J]. Journal of Yunnan University: Natural Sciences Edition, 2020, 42(6): 1027-1037. DOI: 10.7540/j.ynu.20200385

广义部分函数型线性模型的多项式样条估计

Polynomial spline estimation for generalized partial functional linear regression models

  • 摘要: 考虑到样条估计方法的计算效率和估计结果的光滑性,研究了广义部分函数型线性模型的多项式样条估计. 在一定的正则条件下,获得了参数估计的渐近正态性及斜率函数估计的全局收敛速度. 通过模拟研究,说明了估计方法的有效性,同时发现当真实斜率函数光滑且不能表示成少数特征函数线性组合时,样条估计优于函数型主成分估计.

     

    Abstract: Considering its computational efficiency and smoothness, the polynomial spline estimation of generalized partial functional linear models is studied. Under some regular conditions, the asymptotic normality of parameter estimation and the global convergence rate of slope function have been established. By simulation study, the validity of the estimation method is illustrated. At the same time, it is found that the spline estimation is superior to the functional principal component estimation while the true slope function is smooth and can not be expressed as a linear combination of a few eigenfunctions.

     

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