M-Estimation for partially functional linear regression model based on splines
M-Estimation for partially functional linear regression model based on splines
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DOI：
10.1080/03610926.2014.921309
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发表时间：
2016-08
期刊：
影响因子：
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通讯作者：
Jianjun Zhou;Jiang Du;Zhimeng Sun
中科院分区：
文献类型：
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作者：
Jianjun Zhou;Jiang Du;Zhimeng Sun
摘要M-估计是一种广泛使用的稳健统计推断技术。本文研究了一个尺度响应变量由一个函数值变量和有限个实值变量来解释的稳健部分泛函线性回归模型。对于回归参数的估计，我们使用多项式样条来逼近斜率参数，回归参数包括无穷维函数和实值变量的斜率参数。该估计过程易于实现，对响应中的重尾误差或异常值具有较强的抵抗力。建立了所提出的估计量的渐近性质。最后，通过蒙特卡罗模拟研究，对该方法的有限样本性能进行了评估。
ABSTRACT M-estimation is a widely used technique for robust statistical inference. In this paper, we study robust partially functional linear regression model in which a scale response variable is explained by a function-valued variable and a finite number of real-valued variables. For the estimation of the regression parameters, which include the infinite dimensional function as well as the slope parameters for the real-valued variables, we use polynomial splines to approximate the slop parameter. The estimation procedure is easy to implement, and it is resistant to heavy-tailederrors or outliers in the response. The asymptotic properties of the proposed estimators are established. Finally, we assess the finite sample performance of the proposed method by Monte Carlo simulation studies.