Communications for Statistical Applications and Methods

  • 제27권1호
  • /
  • Pages.149-161
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  • 2020
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  • 2287-7843(pISSN)
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  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
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Principal component analysis for Hilbertian functional data

  • Kim, Dongwoo (Department of Statistics, Seoul National University) ;
  • Lee, Young Kyung (Department of Information Statistics, Kangwon National University) ;
  • Park, Byeong U. (Department of Statistics, Seoul National University)
  • 투고 : 2019.11.11
  • 심사 : 2019.12.03
  • 발행 : 2020.01.31
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초록

In this paper we extend the functional principal component analysis for real-valued random functions to the case of Hilbert-space-valued functional random objects. For this, we introduce an autocovariance operator acting on the space of real-valued functions. We establish an eigendecomposition of the autocovariance operator and a Karuhnen-Loève expansion. We propose the estimators of the eigenfunctions and the functional principal component scores, and investigate the rates of convergence of the estimators to their targets. We detail the implementation of the methodology for the cases of compositional vectors and density functions, and illustrate the method by analyzing time-varying population composition data. We also discuss an extension of the methodology to multivariate cases and develop the corresponding theory.

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과제정보

연구 과제 주관 기관 : National Research Foundation of Korea (NRF)

Research of Young Kyung Lee was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2018R1A2B6001068). Research of Dongwoo Kim and Byeong U. Park was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (No. 2019R1A2C3007355).

참고문헌

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