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    Selecting the Number of Principal Components in Functional Data

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    Type
    Article
    Authors
    Li, Yehua
    Wang, Naisyin
    Carroll, Raymond J.
    KAUST Grant Number
    KUS-CI-016-04
    Date
    2013-12
    Permanent link to this record
    http://hdl.handle.net/10754/599572
    
    Metadata
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    Abstract
    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. © 2013 American Statistical Association.
    Citation
    Li 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.
    Sponsors
    Li'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.
    Publisher
    Informa UK Limited
    Journal
    Journal of the American Statistical Association
    DOI
    10.1080/01621459.2013.788980
    PubMed ID
    24376287
    PubMed Central ID
    PMC3872138
    ae974a485f413a2113503eed53cd6c53
    10.1080/01621459.2013.788980
    Scopus Count
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