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Parametric functional principal component analysis
Author(s) -
Sang Peijun,
Wang Liangliang,
Cao Jiguo
Publication year - 2017
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/biom.12641
Subject(s) - principal component analysis , functional principal component analysis , parametric statistics , component (thermodynamics) , computer science , mathematics , econometrics , statistics , physics , thermodynamics
Summary Functional principal component analysis (FPCA) is a popular approach in functional data analysis to explore major sources of variation in a sample of random curves. These major sources of variation are represented by functional principal components (FPCs). Most existing FPCA approaches use a set of flexible basis functions such as B‐spline basis to represent the FPCs, and control the smoothness of the FPCs by adding roughness penalties. However, the flexible representations pose difficulties for users to understand and interpret the FPCs. In this article, we consider a variety of applications of FPCA and find that, in many situations, the shapes of top FPCs are simple enough to be approximated using simple parametric functions. We propose a parametric approach to estimate the top FPCs to enhance their interpretability for users. Our parametric approach can also circumvent the smoothing parameter selecting process in conventional nonparametric FPCA methods. In addition, our simulation study shows that the proposed parametric FPCA is more robust when outlier curves exist. The parametric FPCA method is demonstrated by analyzing several datasets from a variety of applications.