相依误差下部分函数型线性模型的估计

Partial Functional Linear Models with Dependent Errors

本文研究当误差序列为平稳的a-混合序列时,部分函数型线性模型的估计问题,基于用Karhunen-Loeve展开来逼近斜率函数的思想,给出了未知参数和斜率函数的估计方法,并进一步建立了参数估计量的渐近正态性和斜率函数估计量的收敛速度.最后用模拟研究和具体实例说明了估计方法的良好表现以及相依误差结构对估计量所带来的影响.

In this paper, we study the estimation of partial functional linear regression models with stationary α-mixing random error sequence. With approximating to the slope function by the Karhunen-Loeve expansion, we propose an estimation method for the unknown parameters and the slope function. The asymptotic normality of the proposed parameter estimators and the convergence rate of the slope function estimator are established. Intensive simulation experiments and real data analysis are conducted to show that the proposed method performs well with a finite sample.