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Asymptotic properties of principal component projections with repeated eigenvalues

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  • Petrovich, Justin
  • Reimherr, Matthew

Abstract

In FPCA methods, it is common to assume that the eigenvalues are distinct in order to facilitate theoretical proofs. We relax this assumption, provide a stochastic expansion for the estimated functional principal component projections, and establish their asymptotic normality.

Suggested Citation

  • Petrovich, Justin & Reimherr, Matthew, 2017. "Asymptotic properties of principal component projections with repeated eigenvalues," Statistics & Probability Letters, Elsevier, vol. 130(C), pages 42-48.
    • Handle: RePEc:eee:stapro:v:130:y:2017:i:c:p:42-48
    DOI: 10.1016/j.spl.2017.07.004
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    1. Crainiceanu, Ciprian M. & Staicu, Ana-Maria & Di, Chong-Zhi, 2009. "Generalized Multilevel Functional Regression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1550-1561.
    2. Hervé Cardot & Frédéric Ferraty & André Mas & Pascal Sarda, 2003. "Testing Hypotheses in the Functional Linear Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 241-255, March.
    3. Julien Jacques & Cristian Preda, 2014. "Functional data clustering: a survey," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(3), pages 231-255, September.
    4. Han Shang, 2014. "A survey of functional principal component analysis," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(2), pages 121-142, April.
    5. Dehan Kong & Ana-Maria Staicu & Arnab Maity, 2016. "Classical testing in functional linear models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(4), pages 813-838, October.
    6. Aurore Delaigle & Peter Hall, 2012. "Achieving near perfect classification for functional data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(2), pages 267-286, March.
    7. Reimherr, Matthew, 2015. "Functional regression with repeated eigenvalues," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 62-70.
    8. Chen, Xiaohong & White, Halbert, 1998. "Central Limit And Functional Central Limit Theorems For Hilbert-Valued Dependent Heterogeneous Arrays With Applications," Econometric Theory, Cambridge University Press, vol. 14(2), pages 260-284, April.
    9. J. Goldsmith & S. Greven & C. Crainiceanu, 2013. "Corrected Confidence Bands for Functional Data Using Principal Components," Biometrics, The International Biometric Society, vol. 69(1), pages 41-51, March.
    10. Kokoszka, Piotr & Reimherr, Matthew, 2013. "Asymptotic normality of the principal components of functional time series," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1546-1562.
    11. Horváth, Lajos & Hušková, Marie & Rice, Gregory, 2013. "Test of independence for functional data," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 100-119.
    12. Peter Hall & Mohammad Hosseini‐Nasab, 2006. "On properties of functional principal components analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 109-126, February.
    13. Siegfried Hörmann & Łukasz Kidziński, 2015. "A Note on Estimation in Hilbertian Linear Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 43-62, March.
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