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http://dx.doi.org/10.5351/KJAS.2019.32.4.607

Classical testing based on B-splines in functional linear models  

Sohn, Jihoon (Korea Credit Bureau Co., Ltd)
Lee, Eun Ryung (Department of Statistics, Sungkyunkwan University)
Publication Information
The Korean Journal of Applied Statistics / v.32, no.4, 2019 , pp. 607-618 More about this Journal
Abstract
A new and interesting task in statistics is to effectively analyze functional data that frequently comes from advances in modern science and technology in areas such as meteorology and biomedical sciences. Functional linear regression with scalar response is a popular functional data analysis technique and it is often a common problem to determine a functional association if a functional predictor variable affects the scalar response in the models. Recently, Kong et al. (Journal of Nonparametric Statistics, 28, 813-838, 2016) established classical testing methods for this based on functional principal component analysis (of the functional predictor), that is, the resulting eigenfunctions (as a basis). However, the eigenbasis functions are not generally suitable for regression purpose because they are only concerned with the variability of the functional predictor, not the functional association of interest in testing problems. Additionally, eigenfunctions are to be estimated from data so that estimation errors might be involved in the performance of testing procedures. To circumvent these issues, we propose a testing method based on fixed basis such as B-splines and show that it works well via simulations. It is also illustrated via simulated and real data examples that the proposed testing method provides more effective and intuitive results due to the localization properties of B-splines.
Keywords
functional linear regression; functional association test; Wald test; functional principal component analysis; eigenfunctions; B-spline basis;
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