Selecting the Number of Principal Components in Functional Data
成果类型：
Article
署名作者：
Li, Yehua; Wang, Naisyin; Carroll, Raymond J.
署名单位：
Iowa State University; University of Michigan System; University of Michigan; Texas A&M University System; Texas A&M University College Station
刊物名称：
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN/ISSBN：
0162-1459
DOI：
10.1080/01621459.2013.788980
发表日期：
2013
页码：
1284-1294
关键词：
colon carcinogenesis
longitudinal data
Nonparametric Regression
linear-regression
models
dimensionality
reduction
CURVES
摘要：
Functional principal component analysis (FPCA) has become the most widely used dimension reduction tool for functional data analysis. We consider functional data measured at random, subject-specific time points, contaminated with measurement error, allowing for both sparse and dense functional data, and propose novel information criteria to select the number of principal component in such data. We propose a Bayesian information criterion based on marginal modeling that can consistently select the number of principal components for both sparse and dense functional data. For dense functional data, we also develop an Akaike information criterion based on the expected Kullback-Leibler information under a Gaussian assumption. In connecting with the time series literature, we also consider a class of information criteria proposed for factor analysis of multivariate time series and show that they are still consistent for dense functional data, if a prescribed undersmoothing scheme is undertaken in the FPCA algorithm. We perform intensive simulation studies and show that the proposed information criteria vastly outperform existing methods for this type of data. Surprisingly, our empirical evidence shows that our information criteria proposed for dense functional data also perform well for sparse functional data. An empirical example using colon carcinogenesis data is also provided to illustrate the results. Supplementary materials for this article are available online.