We propose a new estimation procedure for estimating the unknown parameters and function in partial functional linear regression. The asymptotic distribution of the estimator of the vector of slope parameters is derived, and the global convergence rate of the estimator of unknown slope function is established under suitable norm. The convergence rate of the mean squared prediction error for the proposed estimators is also established. Based on the proposed estimation procedure, we further construct the penalized regression estimators and establish their variable selection consistency and oracle properties. Finite sample properties of our procedures are studied through Monte Carlo simulations. A real data example about the real estate data is used to illustrate our proposed methodology.

中文翻译：

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部分函数线性回归的估计和变量选择

我们提出了一种新的估计程序，用于估计部分函数线性回归中的未知参数和函数。推导了斜率参数向量估计量的渐近分布，并在适当的范数下建立了未知斜率函数估计量的全局收敛速度。还确定了所提出的估计量的均方预测误差的收敛速度。基于提出的估计程序，我们进一步构造了惩罚回归估计量，并建立了它们的变量选择一致性和预言性。通过蒙特卡洛模拟研究了我们程序的有限样本属性。一个有关房地产数据的真实数据示例用于说明我们提出的方法。