Estimation and Hypothesis Test for Mean Curve with Functional Data by Reproducing Kernel Hilbert Space Methods, with Applications in Biostatistics

Ming Xiong, Ao Yuan (), Hong-Bin Fang, Colin O. Wu and Ming T. Tan ()
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Ming Xiong: School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China
Ao Yuan: Department of Biostatistics, Bioinformatics and Biomathematics, Georgetown University, Washington, DC 20057, USA
Hong-Bin Fang: Department of Biostatistics, Bioinformatics and Biomathematics, Georgetown University, Washington, DC 20057, USA
Colin O. Wu: National Heart, Lung and Blood Institute, Office of Biostatistics Research, Bethesda, MD 20892, USA
Ming T. Tan: Department of Biostatistics, Bioinformatics and Biomathematics, Georgetown University, Washington, DC 20057, USA

Mathematics, 2022, vol. 10, issue 23, 1-17

Abstract: Functional data analysis has important applications in biomedical, health studies and other areas. In this paper, we develop a general framework for a mean curve estimation for functional data using a reproducing kernel Hilbert space (RKHS) and derive its asymptotic distribution theory. We also propose two statistics for testing the equality of mean curves from two populations and a mean curve belonging to some subspace, respectively. Simulation studies are conducted to evaluate the performance of the proposed method and are compared with the major existing methods, which shows that the proposed method has a better performance than the existing ones. The method is then illustrated with an analysis of the growth data from the National Growth and Health Study (NGHS) project sponsored by the NIH.

Keywords: functional data; hypothesis testing; kernel function; mean curve estimation; reproducing kernel Hilbert space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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