Empirical Likelihood Inference for Partial Functional Linear Regression Models Based on B-spline

Mingao Yuan,Yue Zhang

doi:10.5539/ijsp.v8n1p135

Abstract

In this paper, we apply empirical likelihood method to infer for the regression parameters in the partial functional linear regression models based on B-spline. We prove that the empirical log-likelihood ratio for the regression parameters converges in law to a weighted sum of independent chi-square distributions. Our simulation shows that the proposed empirical likelihood method produces more accurate confidence regions in terms of coverage probability than the asymptotic normality method.

Highlights

With the rapid development of measurement apparatus and computers, it is possible that the data are collected over an entire time period
We apply empirical likelihood method to infer for the regression parameters in the partial functional linear regression models based on B-spline
We prove that the empirical log-likelihood ratio for the regression parameters converges in law to a weighted sum of independent chi-square distributions

Summary

Introduction

With the rapid development of measurement apparatus and computers, it is possible that the data are collected over an entire time period. One of them is the functional principle component analysis (FPCA), which has the advantages of interpretability and availability of a good estimate of the slope function (Cai and Hall (2006), Hall and Horowit (2007), Shin (2009), Yuan and Cai (2010), Cai and Yuan (2012)) Another approach is the polynomial spline method. For estimators based on B-spline in partial functional linear model, Zhou et al (2016) established the asymptotic normality for the regression parameters and the global convergence rate for the slope function. We propose the empirical likelihood based confidence region for the regression parameters in partial functional linear model and compare it with the ones based on asymptotic normality proposed in Zhou et al (2016).

Asymptotic Normality Method The partial functional linear model is

The Empirical Likelihood Method

Simulation Study

Discussion