Author(s)

Yafei Wang, Tianfa Xie, Zhongzhan Zhang

College of Applied Sciences, Beijing University of Technology, Beijing, China.

In this paper, the estimation of the parameters in partial functional linear models with ARCH(p) errors is discussed. With employing the functional principle component, a hybrid estimating method is suggested. The asymptotic normality of the proposed estimators for both the linear parameter in the mean model and the parameter in the ARCH error model is obtained, and the convergence rate of the slope function estimate is established. Besides, some simulations and a real data analysis are conducted for illustration, and it is shown that the proposed method performs well with a finite sample.

Asymptotic Normality, ARCH(p) Errors, Functional Principal Components, Convergence Rate, Least Absolute Deviation

Wang, Y. , Xie, T. and Zhang, Z. (2018) Partial Functional Linear Models with ARCH Errors. Open Journal of Statistics, 8, 345-361. doi: 10.4236/ojs.2018.82023.