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
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).
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Statistics and Probability
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
