메뉴 건너뛰기




Volumn 40, Issue 5, 2012, Pages 2483-2510

Sampled forms of functional PCA in reproducing kernel hilbert spaces

Author keywords

Fourier truncation; Functional principal component analysis; Linear sampling operator; Reproducing kernel Hilbert space; Time sampling

Indexed keywords


EID: 84873374810     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/12-AOS1033     Document Type: Article
Times cited : (26)

References (32)
  • 1
    • 69049101180 scopus 로고    scopus 로고
    • High-dimensional analysis of semidefinite relaxations for sparse principal components
    • MR2541450
    • AMINI, A. A. and WAINWRIGHT, M. J. (2009). High-dimensional analysis of semidefinite relaxations for sparse principal components. Ann. Statist. 37 2877-2921. MR2541450
    • (2009) Ann. Statist. , vol.37 , pp. 2877-2921
    • Amini, A.A.1    Wainwright, M.J.2
  • 2
    • 84155166978 scopus 로고    scopus 로고
    • Approximation properties of certain operatorinduced norms on Hilbert spaces
    • MR2864648
    • AMINI, A. A. and WAINWRIGHT, M. J. (2012). Approximation properties of certain operatorinduced norms on Hilbert spaces. J. Approx. Theory 164 320-345. MR2864648
    • (2012) J. Approx. Theory , vol.164 , pp. 320-345
    • Amini, A.A.1    Wainwright, M.J.2
  • 5
    • 0001181674 scopus 로고
    • Principal components analysis of sampled functions
    • MR0848110
    • BESSE, P. and RAMSAY, J. O. (1986). Principal components analysis of sampled functions. Psychometrika 51 285-311. MR0848110
    • (1986) Psychometrika , vol.51 , pp. 285-311
    • Besse, P.1    Ramsay, J.O.2
  • 7
    • 0010741912 scopus 로고    scopus 로고
    • Kernel-based functional principal components
    • MR1771495
    • BOENTE, G. and FRAIMAN, R. (2000). Kernel-based functional principal components. Statist. Probab. Lett. 48 335-345. MR1771495
    • (2000) Statist. Probab. Lett. , vol.48 , pp. 335-345
    • Boente, G.1    Fraiman, R.2
  • 10
    • 0001469917 scopus 로고    scopus 로고
    • Nonparametric estimation of smoothed principal components analysis of sampled noisy functions
    • MR1785396
    • CARDOT, H. (2000). Nonparametric estimation of smoothed principal components analysis of sampled noisy functions. J. Nonparametr. Stat. 12 503-538. MR1785396
    • (2000) J. Nonparametr. Stat. , vol.12 , pp. 503-538
    • Cardot, H.1
  • 11
    • 0000957849 scopus 로고
    • Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference
    • MR0650934
    • DAUXOIS, J., POUSSE, A. and ROMAIN, Y. (1982). Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference. J. Multivariate Anal. 12 136-154. MR0650934
    • (1982) J. Multivariate Anal. , vol.12 , pp. 136-154
    • Dauxois, J.1    Pousse, A.2    Romain, Y.3
  • 12
    • 0012070851 scopus 로고    scopus 로고
    • Local operator theory, random matrices and Banach spaces
    • North-Holland Amsterdam MR1863696
    • DAVIDSON, K. R. and SZAREK, S. J. (2001). Local operator theory, random matrices and Banach spaces. In Handbook of the Geometry of Banach Spaces, Vol. I 317-366. North- Holland, Amsterdam. MR1863696
    • (2001) Handbook of the Geometry of Banach Spaces , vol.1 , pp. 317-366
    • Davidson, K.R.1    Szarek, S.J.2
  • 15
    • 33645039219 scopus 로고    scopus 로고
    • On properties of functional principal components analysis
    • MR2212577
    • HALL, P. and HOSSEINI-NASAB, M. (2006). On properties of functional principal components analysis. J. R. Stat. Soc. Ser. B Stat. Methodol. 68 109-126. MR2212577
    • (2006) J. R. Stat. Soc. Ser. B Stat. Methodol. , vol.68 , pp. 109-126
    • Hall, P.1    Hosseini-Nasab, M.2
  • 16
    • 33747153005 scopus 로고    scopus 로고
    • Properties of principal component methods for functional and longitudinal data analysis
    • MR2278365
    • HALL, P.,MÜLLER, H.-G. and WANG, J.-L. (2006). Properties of principal component methods for functional and longitudinal data analysis. Ann. Statist. 34 1493-1517. MR2278365
    • (2006) Ann. Statist. , vol.34 , pp. 1493-1517
    • Hall, P.1    Müller, H.-G.2    Wang, J.-L.3
  • 17
    • 69249142337 scopus 로고    scopus 로고
    • Functional principal components analysis via penalized rank one approximation
    • MR2426107
    • HUANG, J. Z., SHEN, H. and BUJA, A. (2008). Functional principal components analysis via penalized rank one approximation. Electron. J. Stat. 2 678-695. MR2426107
    • (2008) Electron. J. Stat. , vol.2 , pp. 678-695
    • Huang, J.Z.1    Shen, H.2    Buja, A.3
  • 18
    • 0035641726 scopus 로고    scopus 로고
    • On the distribution of the largest eigenvalue in principal components analysis
    • MR1863961
    • JOHNSTONE, I. M. (2001). On the distribution of the largest eigenvalue in principal components analysis. Ann. Statist. 29 295-327. MR1863961
    • (2001) Ann. Statist. , vol.29 , pp. 295-327
    • Johnstone, I.M.1
  • 19
    • 66549088006 scopus 로고    scopus 로고
    • On consistency and sparsity for principal components analysis in high dimensions
    • MR2751448
    • JOHNSTONE, I. M. and LU, A. Y. (2009). On consistency and sparsity for principal components analysis in high dimensions. J. Amer. Statist. Assoc. 104 682-693. MR2751448
    • (2009) J. Amer. Statist. Assoc. , vol.104 , pp. 682-693
    • Johnstone, I.M.1    A, Y.L.U.2
  • 21
    • 78650108606 scopus 로고    scopus 로고
    • Uniform convergence rates for nonparametric regression and principal component analysis in functional/longitudinal data
    • MR2766854
    • LI, Y. and HSING, T. (2010). Uniform convergence rates for nonparametric regression and principal component analysis in functional/longitudinal data. Ann. Statist. 38 3321-3351. MR2766854
    • (2010) Ann. Statist. , vol.38 , pp. 3321-3351
    • I, Y.L.1    Hsing, T.2
  • 24
    • 0001919174 scopus 로고
    • Some properties of smoothed principal components analysis for functional data
    • MR1220336
    • PEZZULLI, S. and SILVERMAN, B. W. (1993). Some properties of smoothed principal components analysis for functional data. Comput. Statist. 8 1-16. MR1220336
    • (1993) Comput. Statist. , vol.8 , pp. 1-16
    • Pezzulli, S.1    Silverman, B.W.2
  • 28
    • 0001597980 scopus 로고
    • Estimating the mean and covariance structure nonparametrically when the data are curves
    • MR1094283
    • RICE, J. A. and SILVERMAN, B. W. (1991). Estimating the mean and covariance structure nonparametrically when the data are curves. J. R. Stat. Soc. Ser. B Stat. Methodol. 53 233-243. MR1094283
    • (1991) J. R. Stat. Soc. Ser. B Stat. Methodol. , vol.53 , pp. 233-243
    • Rice, J.A.1    Silverman, B.W.2
  • 29
    • 0030537857 scopus 로고    scopus 로고
    • Smoothed functional principal components analysis by choice of norm
    • MR1389877
    • SILVERMAN, B. W. (1996). Smoothed functional principal components analysis by choice of norm. Ann. Statist. 24 1-24. MR1389877
    • (1996) Ann. Statist. , vol.24 , pp. 1-24
    • Silverman, B.W.1
  • 32
    • 19744375466 scopus 로고    scopus 로고
    • Functional data analysis for sparse longitudinal data
    • MR2160561
    • YAO, F.,MÜLLER, H.-G. and WANG, J.-L. (2005). Functional data analysis for sparse longitudinal data. J. Amer. Statist. Assoc. 100 577-590. MR2160561
    • (2005) J. Amer. Statist. Assoc. , vol.100 , pp. 577-590
    • Yao, F.1    Müller, H.-G.2    Wang, J.-L.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.