메뉴 건너뛰기




Volumn 37, Issue 2, 2009, Pages 569-595

A data-driven block thresholding approach to wavelet estimation

Author keywords

Adaptivity; Besov body; Block thresholding; James stein estimator; Nonparametric regression; Stein's unbiased risk estimate; Wavelets

Indexed keywords


EID: 65349108741     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/07-AOS538     Document Type: Article
Times cited : (78)

References (27)
  • 1
    • 0442312210 scopus 로고    scopus 로고
    • Regularization of wavelet approximations (with discussion)
    • MR1946364
    • ANTONIADIS, A. and FAN, J. (2001). Regularization of wavelet approximations (with discussion). J. Amer. Statist. Assoc. 96 939-967. MR1946364
    • (2001) J. Amer. Statist. Assoc , vol.96 , pp. 939-967
    • ANTONIADIS, A.1    FAN, J.2
  • 2
    • 84874257732 scopus 로고
    • Better subset regression using the nonnegative garrote
    • MR1365720
    • BREIMAN, L. (1995). Better subset regression using the nonnegative garrote. Technometrics 37 373-384. MR1365720
    • (1995) Technometrics , vol.37 , pp. 373-384
    • BREIMAN, L.1
  • 3
    • 0033248624 scopus 로고    scopus 로고
    • Adaptive wavelet estimation: A block thresholding and oracle inequality approach
    • MR1724035
    • CAI, T. (1999). Adaptive wavelet estimation: A block thresholding and oracle inequality approach. Ann. Statist. 27 898-924. MR1724035
    • (1999) Ann. Statist , vol.27 , pp. 898-924
    • CAI, T.1
  • 4
    • 65349168489 scopus 로고    scopus 로고
    • CAI, T., LOW, M. G. and ZHAO, L. (2000). Blockwise thresholding methods for sharp adaptive estimation. Technical report, Dept. Statistics, Univ. Pennsylvania.
    • CAI, T., LOW, M. G. and ZHAO, L. (2000). Blockwise thresholding methods for sharp adaptive estimation. Technical report, Dept. Statistics, Univ. Pennsylvania.
  • 5
    • 0001298787 scopus 로고    scopus 로고
    • Incorporating information on neighboring coefficients into wavelet estimation
    • MR1895786
    • CAI, T. and SILVERMAN, B. W. (2001). Incorporating information on neighboring coefficients into wavelet estimation. Sankhyā Ser. B 63 127-148. MR1895786
    • (2001) Sankhyā Ser. B , vol.63 , pp. 127-148
    • CAI, T.1    SILVERMAN, B.W.2
  • 7
    • 16644374768 scopus 로고    scopus 로고
    • Block-dependent thresholding in wavelet regression
    • MR2130851
    • CHICKEN, E. (2005). Block-dependent thresholding in wavelet regression. J. Nonparametr. Statist. 17 467-491. MR2130851
    • (2005) J. Nonparametr. Statist , vol.17 , pp. 467-491
    • CHICKEN, E.1
  • 8
    • 18744367828 scopus 로고    scopus 로고
    • Block thresholding for density estimation: Local and global adaptivity
    • MR2164124
    • CHICKEN, E. and CAI, T. (2005). Block thresholding for density estimation: Local and global adaptivity. J. Multivariate Anal. 95 76-106. MR2164124
    • (2005) J. Multivariate Anal , vol.95 , pp. 76-106
    • CHICKEN, E.1    CAI, T.2
  • 9
    • 65349088098 scopus 로고    scopus 로고
    • DAUBECHIES, I. (1992). Ten Lectures on Wavelets. SIAM, Philadelphia, PA. MR1162107
    • DAUBECHIES, I. (1992). Ten Lectures on Wavelets. SIAM, Philadelphia, PA. MR1162107
  • 10
    • 65349097561 scopus 로고    scopus 로고
    • DEVORE, R. and LORENTZ, G. G. (1993). Constructive Approximation. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 303. Springer, Berlin. MR1261635
    • DEVORE, R. and LORENTZ, G. G. (1993). Constructive Approximation. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 303. Springer, Berlin. MR1261635
  • 11
    • 0041958932 scopus 로고
    • Ideal spatial adaptation by wavelet shrinkage
    • MR1311089
    • DONOHO, D. L. and JOHNSTONE, I. M. (1994a). Ideal spatial adaptation by wavelet shrinkage. Biometrika 81 425-455. MR1311089
    • (1994) Biometrika , vol.81 , pp. 425-455
    • DONOHO, D.L.1    JOHNSTONE, I.M.2
  • 12
    • 0012499079 scopus 로고
    • Minimax risk over lp-balls for lq -error
    • MR1278886
    • DONOHO, D. L. and JOHNSTONE, I. M. (1994b). Minimax risk over lp-balls for lq -error. Probab. Theory Related Fields 99 277-303. MR1278886
    • (1994) Probab. Theory Related Fields , vol.99 , pp. 277-303
    • DONOHO, D.L.1    JOHNSTONE, I.M.2
  • 13
    • 84950459514 scopus 로고
    • Adapt to unknown smoothness via wavelet shrinkage
    • MR1379464
    • DONOHO, D. L. and JOHNSTONE, I. M. (1995). Adapt to unknown smoothness via wavelet shrinkage. J. Amer. Statist. Assoc. 90 1200-1224. MR1379464
    • (1995) J. Amer. Statist. Assoc , vol.90 , pp. 1200-1224
    • DONOHO, D.L.1    JOHNSTONE, I.M.2
  • 14
    • 0032334093 scopus 로고    scopus 로고
    • Minimax estimation via wavelet shrinkage
    • MR1635414
    • DONOHO, D. L. and JOHNSTONE, I. M. (1998). Minimax estimation via wavelet shrinkage. Ann. Statist. 26 879-921. MR1635414
    • (1998) Ann. Statist , vol.26 , pp. 879-921
    • DONOHO, D.L.1    JOHNSTONE, I.M.2
  • 15
    • 0001014229 scopus 로고
    • Minimax risk over hyperrectangles, and implications
    • MR1062717
    • DONOHO, D. L., LIU, R. C. andMACG IBBON, B. (1990). Minimax risk over hyperrectangles, and implications. Ann. Statist. 18 1416-1437. MR1062717
    • (1990) Ann. Statist , vol.18 , pp. 1416-1437
    • DONOHO, D.L.1    LIU, R.C.2    andMACG3    IBBON, B.4
  • 16
    • 0012722713 scopus 로고
    • Nonparametric estimation of a density of unknown smoothness
    • MR0805304
    • EFROMOVICH, S. Y. (1985). Nonparametric estimation of a density of unknown smoothness. Theor. Probab. Appl. 30 557-661. MR0805304
    • (1985) Theor. Probab. Appl , vol.30 , pp. 557-661
    • EFROMOVICH, S.Y.1
  • 17
    • 0032282297 scopus 로고    scopus 로고
    • Wavelet shrinkage denoising using the nonnegative garrote
    • MR1665666
    • GAO, H.-Y. (1998). Wavelet shrinkage denoising using the nonnegative garrote. J. Comput. Graph. Statist. 7 469-488. MR1665666
    • (1998) J. Comput. Graph. Statist , vol.7 , pp. 469-488
    • GAO, H.-Y.1
  • 18
    • 0032360314 scopus 로고    scopus 로고
    • Block threshold rules for curve estimation using kernel and wavelet methods
    • MR1635418
    • HALL, P., KERKYACHARIAN, G. and PICARD, D. (1998). Block threshold rules for curve estimation using kernel and wavelet methods. Ann. Statist. 26 922-942. MR1635418
    • (1998) Ann. Statist , vol.26 , pp. 922-942
    • HALL, P.1    KERKYACHARIAN, G.2    PICARD, D.3
  • 19
    • 0347181848 scopus 로고    scopus 로고
    • On the minimax optimality of block thresholded wavelet estimators
    • MR1678880
    • HALL, P., KERKYACHARIAN, G. and PICARD, D. (1999). On the minimax optimality of block thresholded wavelet estimators. Statist. Sinica 9 33-50. MR1678880
    • (1999) Statist. Sinica , vol.9 , pp. 33-50
    • HALL, P.1    KERKYACHARIAN, G.2    PICARD, D.3
  • 20
    • 0033408849 scopus 로고    scopus 로고
    • Wavelet shrinkage for correlated data and inverse problems: Adaptivity results
    • MR1678881
    • JOHNSTONE, I. M. (1999). Wavelet shrinkage for correlated data and inverse problems: Adaptivity results. Statist. Sinica 9 51-84. MR1678881
    • (1999) Statist. Sinica , vol.9 , pp. 51-84
    • JOHNSTONE, I.M.1
  • 21
    • 0007322661 scopus 로고    scopus 로고
    • Function estimation and Gaussian sequence model
    • Unpublished manuscript
    • JOHNSTONE, I. M. (2002). Function estimation and Gaussian sequence model. Unpublished manuscript.
    • (2002)
    • JOHNSTONE, I.M.1
  • 22
    • 18444410406 scopus 로고    scopus 로고
    • JOHNSTONE, I. M. and SILVERMAN, B. W. (2005). Empirical Bayes selection of wavelet thresholds. Ann. Statist. 33 1700-1752. MR2166560
    • JOHNSTONE, I. M. and SILVERMAN, B. W. (2005). Empirical Bayes selection of wavelet thresholds. Ann. Statist. 33 1700-1752. MR2166560
  • 23
    • 0012678648 scopus 로고    scopus 로고
    • Lp adaptive density estimation
    • MR1416864
    • KERKYACHARIAN, G., PICARD, D. and TRIBOULEY, K. (1996). Lp adaptive density estimation. Bernoulli 2 229-247. MR1416864
    • (1996) Bernoulli , vol.2 , pp. 229-247
    • KERKYACHARIAN, G.1    PICARD, D.2    TRIBOULEY, K.3
  • 24
    • 65349133196 scopus 로고    scopus 로고
    • MEYER, Y. (1992). Wavelets and Operators. Cambridge Studies in Advanced Mathematics 37. Cambridge Univ. Press, Cambridge. Translated from the 1990 French original by D. H. Salinger. MR1228209
    • MEYER, Y. (1992). Wavelets and Operators. Cambridge Studies in Advanced Mathematics 37. Cambridge Univ. Press, Cambridge. Translated from the 1990 French original by D. H. Salinger. MR1228209
  • 25
    • 0000169918 scopus 로고
    • Estimation of the mean of a multivariate normal distribution
    • MR0630098
    • STEIN, C. (1981). Estimation of the mean of a multivariate normal distribution. Ann. Statist. 9 1135-1151. MR0630098
    • (1981) Ann. Statist , vol.9 , pp. 1135-1151
    • STEIN, C.1
  • 26
    • 0024921922 scopus 로고
    • Wavelet and dilation equations: A brief introduction
    • MR1025484
    • STRANG, G. (1992). Wavelet and dilation equations: A brief introduction. SIAM Rev. 31 614-627. MR1025484
    • (1992) SIAM Rev , vol.31 , pp. 614-627
    • STRANG, G.1
  • 27
    • 84868925351 scopus 로고    scopus 로고
    • TRIEBEL, H. (1983). Theory of Function Spaces. Monographs in Math. 78. Birkhäuser, Basel. MR0781540
    • TRIEBEL, H. (1983). Theory of Function Spaces. Monographs in Math. 78. Birkhäuser, Basel. MR0781540


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.