Article

Test

, Volume 8, Issue 1, pp 1-73

Robust principal component analysis for functional data

  • N. LocantoreAffiliated withDepartment of Statistics, University of North Carolina
  • , J. S. MarronAffiliated withDepartment of Statistics, University of North Carolina Email author 
  • , D. G. SimpsonAffiliated withDepartment of Statistics, University of Illinois
  • , N. TripoliAffiliated withDepartment of Ophthalmology, University of North Carolina
  • , J. T. ZhangAffiliated withDepartment of Statistics, University of North Carolina
  • , K. L. CohenAffiliated withDepartment of Ophthalmology, University of North Carolina
  • , Graciela BoenteAffiliated withUniversidad de Buenos Aires and CONICET
  • , Ricardo FraimanAffiliated withUniversidad de Buenos Aires and Universidad de San Andrés
  • , Babette BrumbackAffiliated withHarvard School of Public Health
    • , Christophe CrouxAffiliated withUniversité Libre de Bruxelles
    • , Jianqing FanAffiliated withUniversity of California Los Angeles
    • , Alois KneipAffiliated withUniversité Catholique de Louvain
    • , John I. MardenAffiliated withDepartment of Statistics, University of North CarolinaUniversity of Illinois at Urbana-Champaign
    • , Daniel PeñaAffiliated withDepartment of Statistics, University of North CarolinaUniversidad Carlos III de Madrid
    • , Javier PrietoAffiliated withDepartment of Statistics, University of North CarolinaUniversidad Carlos III de Madrid
    • , Jim O. RamsayAffiliated withDepartment of Statistics, University of North CarolinaMcGill University
    • , Mariano J. ValderramaAffiliated withDepartment of Statistics, University of North CarolinaUniversidad de Granada
    • , Ana M. AguileraAffiliated withDepartment of Statistics, University of North CarolinaUniversidad de Granada
    • , N. Locantore
    • , J. S. Marron
    • , D. G. Simpson
    • , N. Tripoli
    • , J. T. Zhang
    • , K. L. Cohen

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract

A method for exploring the structure of populations of complex objects, such as images, is considered. The objects are summarized by feature vectors. The statistical backbone is Principal Component Analysis in the space of feature vectors. Visual insights come from representing the results in the original data space. In an ophthalmological example, endemic outliers motivate the development of a bounded influence approach to PCA.

Key words

cornea curvature maps functional data principal components analysis robust statistics spherical PCA Zernike basis

AMS subject classification

62H99