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

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.

Automated summary

We develop a general framework for mean curve estimation in functional data analysis using RKHS and derive its asymptotic distribution theory. Two statistics for testing equality of mean curves and a mean curve belonging to a subspace are proposed. Simulation studies demonstrate the superior performance of the proposed method compared to existing ones.