메뉴 건너뛰기




Volumn , Issue , 2013, Pages 1-333

Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84939841341     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/9781118762547     Document Type: Book
Times cited : (699)

References (71)
  • 2
    • 5844297152 scopus 로고
    • Theory of reproducing kernels
    • Aronszajn N 1950 Theory of reproducing kernels. Trans. Am. Math. Soc. 68, 337-404.
    • (1950) Trans. Am. Math. Soc. , vol.68 , pp. 337-404
    • Aronszajn, N.1
  • 3
    • 29144446225 scopus 로고
    • Mutual information for Gaussian processes
    • Baker C 1970 Mutual information for Gaussian processes. SIAM J. Appl. Math. 19, 451-458.
    • (1970) SIAM J. Appl. Math. , vol.19 , pp. 451-458
    • Baker, C.1
  • 4
    • 84966251435 scopus 로고
    • Joint measures and cross-covariance operators
    • Baker C 1973 Joint measures and cross-covariance operators. Trans. Am. Math. Soc. 186, 273-289.
    • (1973) Trans. Am. Math. Soc. , vol.186 , pp. 273-289
    • Baker, C.1
  • 6
    • 80051684814 scopus 로고    scopus 로고
    • Cambridge University Press, Cambridge
    • Bass R 2011 Stochastic Processes. Cambridge University Press, Cambridge.
    • (2011) Stochastic Processes
    • Bass, R.1
  • 8
    • 33745156863 scopus 로고    scopus 로고
    • Some theory for Fisher's linear discriminant function, 'naive bayes', and some alternatives when there are many more variables than observations
    • Bickel P and Levina E 2004 Some theory for Fisher's linear discriminant function, 'naive bayes', and some alternatives when there are many more variables than observations. Bernoulli 10, 989-1010.
    • (2004) Bernoulli , vol.10 , pp. 989-1010
    • Bickel, P.1    Levina, E.2
  • 11
    • 0000433118 scopus 로고
    • Boundary value and expansion problems of ordinary linear differential equations
    • Birkhoff G 1908 Boundary value and expansion problems of ordinary linear differential equations. Trans. Am. Math. Soc. 9, 373-395.
    • (1908) Trans. Am. Math. Soc. , vol.9 , pp. 373-395
    • Birkhoff, G.1
  • 12
    • 0010249016 scopus 로고
    • Integration von funktionen, deren werte die elemente eines vektorraumes sind
    • Bochner S 1933 Integration von funktionen, deren werte die elemente eines vektorraumes sind. Fundam. Math. 20, 262-276.
    • (1933) Fundam. Math. , vol.20 , pp. 262-276
    • Bochner, S.1
  • 14
    • 82655181491 scopus 로고    scopus 로고
    • Optimal estimation of the mean function based on discretely sampled functional data: phase transition
    • Cai T and Yuan M 2011 Optimal estimation of the mean function based on discretely sampled functional data: phase transition. Ann. Stat. 39, 2330-2355.
    • (2011) Ann. Stat. , vol.39 , pp. 2330-2355
    • Cai, T.1    Yuan, M.2
  • 15
    • 65349171811 scopus 로고    scopus 로고
    • Smoothing spline estimators for functional linear regression
    • Crambes C, Kneip A and Sarda P 2009 Smoothing spline estimators for functional linear regression. Ann. Stat. 37, 35-72.
    • (2009) Ann. Stat. , vol.37 , pp. 35-72
    • Crambes, C.1    Kneip, A.2    Sarda, P.3
  • 16
    • 0000957849 scopus 로고
    • Asymptotic theory for the principal component analysis of a vector random function: some applications to statistical inference
    • Dauxious 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.
    • (1982) J. Multivariate Anal. , vol.12 , pp. 136-154
    • Dauxious, J.1    Pousse, A.2    Romain, Y.3
  • 17
    • 84966198619 scopus 로고
    • Existence and convergence of probability measures in Banach spaces
    • de Acosta A 1970 Existence and convergence of probability measures in Banach spaces. Trans. Am. Math. Soc. 132, 273-298.
    • (1970) Trans. Am. Math. Soc. , vol.132 , pp. 273-298
    • de Acosta, A.1
  • 19
    • 0004217026 scopus 로고
    • American Mathematical Society, Providence, RI
    • Diestel J and Uhl J 1977 Vector Measures. American Mathematical Society, Providence, RI.
    • (1977) Vector Measures
    • Diestel, J.1    Uhl, J.2
  • 20
    • 33646872796 scopus 로고
    • The reproducing kernel Hilbert space structure of sample paths of Gaussian processes
    • Driscoll M 1973 The reproducing kernel Hilbert space structure of sample paths of Gaussian processes. Z. Wahrscheinlichkeitstheorie verw. Geb. 26, 309-316.
    • (1973) Z. Wahrscheinlichkeitstheorie verw. Geb. , vol.26 , pp. 309-316
    • Driscoll, M.1
  • 22
    • 0004083492 scopus 로고    scopus 로고
    • Probability: Theory and Examples, The Wadsworth & Brooks/Cole Statistics/Probability Series
    • LCCN: 95022544, Duxbury Press
    • Durrett R 1996 Probability: Theory and Examples, The Wadsworth & Brooks/Cole Statistics/Probability Series. Duxbury Press, ISBN: 9780534243180, LCCN: 95022544, http://books.google.com/books?id=kkc/_AQAAIAAJ.
    • (1996)
    • Durrett, R.1
  • 24
    • 0040230979 scopus 로고
    • On the laws of large numbers for nonnegative random variables
    • Etemadi N 1983 On the laws of large numbers for nonnegative random variables. J. Multivariate Anal. 13, 187-193.
    • (1983) J. Multivariate Anal. , vol.13 , pp. 187-193
    • Etemadi, N.1
  • 25
    • 48249103423 scopus 로고    scopus 로고
    • Canonical correlation for stochastic processes
    • Eubank R and Hsing T 2007 Canonical correlation for stochastic processes. Stochastic Processes Appl. 118, 1634-1661.
    • (2007) Stochastic Processes Appl. , vol.118 , pp. 1634-1661
    • Eubank, R.1    Hsing, T.2
  • 28
    • 84985404357 scopus 로고
    • Anote on von Neumann's trace inequality
    • Grigorieff RD1991Anote on von Neumann's trace inequality. Math. Nachr. 151, 327-328.
    • (1991) Math. Nachr. , vol.151 , pp. 327-328
    • Grigorieff, R.D.1
  • 29
    • 33645039219 scopus 로고    scopus 로고
    • On properties of functional principal components analysis
    • Hall P and Hosseini-Nasab M 2005 On properties of functional principal components analysis. J. R. Stat. Soc. Ser. B 68, 109-126.
    • (2005) J. R. Stat. Soc. Ser. B , vol.68 , pp. 109-126
    • Hall, P.1    Hosseini-Nasab, M.2
  • 30
    • 57549119141 scopus 로고    scopus 로고
    • Theory for high-order bounds in functional principal components analysis
    • Hall P and Hosseini-Nasab M 2009 Theory for high-order bounds in functional principal components analysis. Math. Proc. Cambridge Philos. Soc. 146, 225-256.
    • (2009) Math. Proc. Cambridge Philos. Soc. , vol.146 , pp. 225-256
    • Hall, P.1    Hosseini-Nasab, M.2
  • 31
    • 0023830542 scopus 로고
    • Computation of the singular value expansion
    • Hansen P 1988 Computation of the singular value expansion. Computing 40, 185-199.
    • (1988) Computing , vol.40 , pp. 185-199
    • Hansen, P.1
  • 32
    • 0038734117 scopus 로고    scopus 로고
    • Functional canonical correlation analysis for square integrable stochastic processes
    • He G, Muller H and Wang J 2003 Functional canonical correlation analysis for square integrable stochastic processes. J. Multivariate Anal. 85, 54-77.
    • (2003) J. Multivariate Anal. , vol.85 , pp. 54-77
    • He, G.1    Muller, H.2    Wang, J.3
  • 33
    • 0000107975 scopus 로고
    • Relations between two sets of variates
    • Hotelling H 1936 Relations between two sets of variates. Biometrika 28, 321-377.
    • (1936) Biometrika , vol.28 , pp. 321-377
    • Hotelling, H.1
  • 39
    • 0000753192 scopus 로고
    • On the supremum of a Gaussian process
    • Landau H and Shepp L 1970 On the supremum of a Gaussian process. Sankhya Ser. A 32, 369-378.
    • (1970) Sankhya Ser. A , vol.32 , pp. 369-378
    • Landau, H.1    Shepp, L.2
  • 41
    • 0034366751 scopus 로고    scopus 로고
    • Tensor product space ANOVA models
    • Lin Y 2000 Tensor product space ANOVA models. Ann. Stat. 28, 734-755.
    • (2000) Ann. Stat. , vol.28 , pp. 734-755
    • Lin, Y.1
  • 42
    • 78650108606 scopus 로고    scopus 로고
    • Uniform convergence rates for nonparametric regression and principal component analysis of functional/longitudinal data
    • Li Y and Hsing T 2010 Uniform convergence rates for nonparametric regression and principal component analysis of functional/longitudinal data. Ann. Stat. 38, 3321-3351.
    • (2010) Ann. Stat. , vol.38 , pp. 3321-3351
    • Li, Y.1    Hsing, T.2
  • 44
    • 33644940148 scopus 로고    scopus 로고
    • Stochastic processes with sample paths in reproducing kernel Hilbert spaces
    • Lukíc M and Beder J 2001 Stochastic processes with sample paths in reproducing kernel Hilbert spaces. Trans. Am. Math. Soc. 353, 3945-3969.
    • (2001) Trans. Am. Math. Soc. , vol.353 , pp. 3945-3969
    • Lukíc, M.1    Beder, J.2
  • 45
    • 33745440307 scopus 로고    scopus 로고
    • A sufficient condition for the CLT in the space of nuclear operators - application to covariance of random functions
    • Mas A 2006 A sufficient condition for the CLT in the space of nuclear operators - application to covariance of random functions. Stat. Probab. Lett. 76, 1503-1509.
    • (2006) Stat. Probab. Lett. , vol.76 , pp. 1503-1509
    • Mas, A.1
  • 46
    • 0242321167 scopus 로고
    • On properly positive Hermitian matrices
    • Moore H 1916 On properly positive Hermitian matrices. Bull. Am. Math. Soc. 23, 66-67.
    • (1916) Bull. Am. Math. Soc. , vol.23 , pp. 66-67
    • Moore, H.1
  • 47
    • 0018904089 scopus 로고
    • Asymptotic distributions in canonical correlation analysis and other multivariate procedures for nonnormal populations
    • Muirhead R and Waternaux C 1980 Asymptotic distributions in canonical correlation analysis and other multivariate procedures for nonnormal populations. Biometrika 67, 31-43.
    • (1980) Biometrika , vol.67 , pp. 31-43
    • Muirhead, R.1    Waternaux, C.2
  • 48
    • 0000823716 scopus 로고
    • Convergence rates for regularized solutions of integral equalities from discrete noisy data
    • Nychka D and Cox D 1989 Convergence rates for regularized solutions of integral equalities from discrete noisy data. Ann. Stat. 17, 556-572.
    • (1989) Ann. Stat. , vol.17 , pp. 556-572
    • Nychka, D.1    Cox, D.2
  • 50
    • 0000461110 scopus 로고
    • An approach to time series analysis
    • Parzen E 1961 An approach to time series analysis. Ann. Math. Stat. 32, 951-989.
    • (1961) Ann. Math. Stat. , vol.32 , pp. 951-989
    • Parzen, E.1
  • 51
    • 0005043637 scopus 로고
    • Statistical inference on time series by RKHS method
    • Canadian Mathematical Congress, Montreal, (ed. Pyke R)
    • Parzen E 1970 Statistical inference on time series by RKHS method. In 12th Annual Biennial Seminar Canadian Mathematical Congress Proceedings (ed. Pyke R), pp. 1-37, Canadian Mathematical Congress, Montreal.
    • (1970) 12th Annual Biennial Seminar Canadian Mathematical Congress Proceedings , pp. 1-37
    • Parzen, E.1
  • 53
    • 0002553181 scopus 로고
    • Estimation and tests of significance in factor analysis
    • Rao C 1955 Estimation and tests of significance in factor analysis. Psychometrika 20, 93-111.
    • (1955) Psychometrika , vol.20 , pp. 93-111
    • Rao, C.1
  • 56
    • 0001597980 scopus 로고
    • Estimating the mean and covariance structure nonparametrically when the data are curves
    • Rice J and Silverman B 1991 Estimating the mean and covariance structure nonparametrically when the data are curves. J. R. Stat. Soc. Ser. B 53, 233-243.
    • (1991) J. R. Stat. Soc. Ser. B , vol.53 , pp. 233-243
    • Rice, J.1    Silverman, B.2
  • 63
    • 43049109196 scopus 로고    scopus 로고
    • An extension of Fisher's discriminant analysis for stochastic processes
    • Shin H 2008 An extension of Fisher's discriminant analysis for stochastic processes. J. Multivariate Anal. 99, 1191-1216.
    • (2008) J. Multivariate Anal. , vol.99 , pp. 1191-1216
    • Shin, H.1
  • 64
    • 0027879547 scopus 로고
    • On the early history of the singular value decomposition
    • Stewart G 1993 On the early history of the singular value decomposition. SIAM Rev. 35, 551-566.
    • (1993) SIAM Rev. , vol.35 , pp. 551-566
    • Stewart, G.1
  • 65
    • 0000439527 scopus 로고
    • Optimal global rates of convergence for nonparametric regression
    • Stone C 1982 Optimal global rates of convergence for nonparametric regression. Ann. Stat. 10, 1040-1053.
    • (1982) Ann. Stat. , vol.10 , pp. 1040-1053
    • Stone, C.1
  • 66
    • 84966229831 scopus 로고
    • A comparison of the series of Fourier and Birkhoff
    • Stone M 1926 A comparison of the series of Fourier and Birkhoff. Trans. Am. Math. Soc. 28, 695-761.
    • (1926) Trans. Am. Math. Soc. , vol.28 , pp. 695-761
    • Stone, M.1
  • 68
    • 0002242889 scopus 로고
    • On the eigenvalues of sums of Hermitian matrices
    • Thompson R and Freede L 1971 On the eigenvalues of sums of Hermitian matrices. Linear Algebra Appl. 4, 369-376.
    • (1971) Linear Algebra Appl. , vol.4 , pp. 369-376
    • Thompson, R.1    Freede, L.2
  • 69
    • 0008286966 scopus 로고
    • Natural splines functions: their associated eigenvalue problem
    • Utreras FI 1983 Natural splines functions: their associated eigenvalue problem. Numer. Math. 63, 107-117.
    • (1983) Numer. Math. , vol.63 , pp. 107-117
    • Utreras, F.I.1
  • 70
    • 38249028378 scopus 로고
    • Boundary effects on convergence rates for Tikhonov regularization
    • Utreras F 1988 Boundary effects on convergence rates for Tikhonov regularization. J. Approx. Theory 54, 235-249.
    • (1988) J. Approx. Theory , vol.54 , pp. 235-249
    • Utreras, F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.