Abstract

In the presented paper, we introduce a partial functional linear model, where a scalar response variable is explained by a multivariate random variable and a functional random variable, and the relationship between the scalar response and both of the predictors is linear. Besides, the model has autoregressive errors. To estimate the model, we first expand the functional predictor and functional regression parametric on the functional principal component basis, and then estimate the coefficients for multivariate and functional regression parametric by a generalized least squares method. Theoretical properties are presented including the asymptotical normality for the multivariate coefficient and the optimal convergence rate for the functional regression parametric. Simulation studies are used to illustrate these characteristics. The proposed method is also applied on the power forecasting of photovoltaic systems data set.

摘要

在本文中，我们介绍了一个偏函数线性模型，其中标量响应变量由多元随机变量和函数随机变量解释，并且标量响应与两个预测变量之间的关系是线性的。此外，该模型具有自回归误差。为了估计模型，我们首先在泛函主成分基础上扩展泛函预测器和泛函回归参数，然后通过广义最小二乘法估计多元和泛函回归参数的系数。提出了理论性质，包括多元系数的渐近正态性和函数回归参数的最佳收敛速度。模拟研究用于说明这些特征。