KAUST Grant NumberKUS-CI-016-04
MetadataShow full item record
AbstractFunctional 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. © 2013 American Statistical Association.
CitationLi Y, Wang N, Carroll RJ (2013) Selecting the Number of Principal Components in Functional Data. Journal of the American Statistical Association 108: 1284–1294. Available: http://dx.doi.org/10.1080/01621459.2013.788980.
SponsorsLi's research was supported by the National Science Foundation (DMS-1105634, DMS-1317118). Wang's research was supported by a grant from the National Cancer Institute (CA74552). Carroll's research was supported by a grant from the National Cancer Institute (R37-CA057030) and by Award Number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST). The authors thank the associate editor and two anonymous referees for their constructive comments that led to significant improvements in the article.
PublisherInforma UK Limited
PubMed Central IDPMC3872138
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