Partial Functional Linear Models with ARCH Errors

Yafei Wang,Zhongzhan Zhang,Tianfa Xie

doi:10.4236/ojs.2018.82023

Abstract

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.

Highlights

IntroductionIn order to combine the flexibility of linear regression models with the recent methodology for the functional linear regression models, partial functional linear models, which was introduced by [1], is considered as follows:
We study the estimation of the unknown parameters in the joint model of (1.2) and (1.3), and propose a hybrid estimation method with combining the functional principle component analysis in the mean model with the least absolute deviation for the error model
1) From Table 1 and Table 2, with the increasing of sample size n, it can be seen MSEs, mean integrated square error (MISE) decrease in all scenarios that we considered about error

Summary

Introduction

In order to combine the flexibility of linear regression models with the recent methodology for the functional linear regression models, partial functional linear models, which was introduced by [1], is considered as follows:. Reference [3] considered the least square estimator of model (1.1) using the Karhunen-Loève (K-L) expansion to approximate the slope function, established asymptotic properties of the resulting estimation. [14] considered a p-th order autoregression process with ARCH errors; [15] studied the estimation of the partly linear regression models with ARCH(p) errors. We study the estimation of the unknown parameters in the joint model of (1.2) and (1.3), and propose a hybrid estimation method with combining the functional principle component analysis in the mean model with the least absolute deviation for the error model. Some preliminary lemmas and the proofs of the theorems are presented in Appendix

Estimation

Asymptotic Properties

Simulation Studies

Real Data Analysis

Findings

Discussion