메뉴 건너뛰기




Volumn 36, Issue 1, 2008, Pages 310-336

Nonlinear estimation for linear inverse problems with error in the operator

Author keywords

Degree of ill posedness; Galerkin projection method; Matrix compression; Minimax rate; Statistical inverse problem; Wavelet thresholding

Indexed keywords


EID: 44449093772     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053607000000721     Document Type: Article
Times cited : (68)

References (17)
  • 1
    • 0000521350 scopus 로고    scopus 로고
    • Wavelet decomposition approaches to statistical inverse problems
    • MR1627226
    • ABRAMOVICH, F. and SILVERMAN, B. W. (1998). Wavelet decomposition approaches to statistical inverse problems. Biometrika 85 115-129. MR1627226
    • (1998) Biometrika , vol.85 , pp. 115-129
    • ABRAMOVICH, F.1    SILVERMAN, B.W.2
  • 2
    • 33847349358 scopus 로고    scopus 로고
    • Prediction in functional linear regression
    • MR2291496
    • CAI. T. and HALL, P. (2006). Prediction in functional linear regression. Ann. Statist. 342159-2179. MR2291496
    • (2006) Ann. Statist , vol.34 , pp. 2159-2179
    • CAI, T.1    HALL, P.2
  • 3
    • 23244442316 scopus 로고    scopus 로고
    • Adaptive estimation for inverse problems with noisy operators
    • MR2158113
    • CAVALIER, L. and HENGARTNER, N. W. (2005). Adaptive estimation for inverse problems with noisy operators. Inverse Problems 21 1345-1361. MR2158113
    • (2005) Inverse Problems , vol.21 , pp. 1345-1361
    • CAVALIER, L.1    HENGARTNER, N.W.2
  • 4
    • 33846966749 scopus 로고    scopus 로고
    • COHEN, A. (2000). Wavelet methods in numerical analysis. In Handbook of Numerical Analysis 7 417-711. North-Holland. Amsterdam. MR1804747
    • COHEN, A. (2000). Wavelet methods in numerical analysis. In Handbook of Numerical Analysis 7 417-711. North-Holland. Amsterdam. MR1804747
  • 5
    • 25444486950 scopus 로고    scopus 로고
    • Adaptive wavelet Galerkin methods for linear inverse problems
    • MR2114287
    • COHEN, A., HOFFMANN, M. and REISS, M. (2004). Adaptive wavelet Galerkin methods for linear inverse problems. SIAM J. Numer. Anal. 42 1479-1501. MR2114287
    • (2004) SIAM J. Numer. Anal , vol.42 , pp. 1479-1501
    • COHEN, A.1    HOFFMANN, M.2    REISS, M.3
  • 6
    • 33745936993 scopus 로고    scopus 로고
    • Compression techniques for boundary integral equations - asymptotically optimal complexity estimates
    • MR2206435
    • DAHMEN, W., HARBRECHT, H. and SCHNEIDER, R. (2005). Compression techniques for boundary integral equations - asymptotically optimal complexity estimates. SIAM J. Numen Anal. 43 2251-2271. MR2206435
    • (2005) SIAM J. Numen Anal , vol.43 , pp. 2251-2271
    • DAHMEN, W.1    HARBRECHT, H.2    SCHNEIDER, R.3
  • 7
    • 0012070851 scopus 로고    scopus 로고
    • DAVIDSON, K. R. and SZAREK, S. J. (2001). Local operator theory, random matrices and Banach spaces. In Handbook on the Geometry of Banach Spaces 1 (W. B. Johnson and J. Lindenstrauss, eds.) 317-366. North-Holland. Amsterdam. MR1863696
    • DAVIDSON, K. R. and SZAREK, S. J. (2001). Local operator theory, random matrices and Banach spaces. In Handbook on the Geometry of Banach Spaces 1 (W. B. Johnson and J. Lindenstrauss, eds.) 317-366. North-Holland. Amsterdam. MR1863696
  • 8
    • 0000954086 scopus 로고    scopus 로고
    • On minimax wavelet estimators
    • MR1400080
    • DELYON, B. and JUDITSKY. A. (1996). On minimax wavelet estimators. Appl. Comput. Harmon. Anal. 3 215-228. MR1400080
    • (1996) Appl. Comput. Harmon. Anal , vol.3 , pp. 215-228
    • DELYON, B.1    JUDITSKY, A.2
  • 9
    • 0029288068 scopus 로고
    • Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition
    • MR1325535
    • DONOHO, D. (1995). Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition. Appl. Comput. Harmon. Anal. 2 101-126. MR1325535
    • (1995) Appl. Comput. Harmon. Anal , vol.2 , pp. 101-126
    • DONOHO, D.1
  • 10
    • 84950459514 scopus 로고
    • Adapting to unknown smoothness via wavelet shrinkage
    • MR1379464
    • DGNOHO, D. L. and JOHNSTONE, I. M. (1995). Adapting to unknown smoothness via wavelet shrinkage. J. Amer. Statist. Assoc. 90 1200-1224. MR1379464
    • (1995) J. Amer. Statist. Assoc , vol.90 , pp. 1200-1224
    • DGNOHO, D.L.1    JOHNSTONE, I.M.2
  • 11
    • 0035504696 scopus 로고    scopus 로고
    • On inverse problems with unknown operators
    • MR1872847
    • EFROMOVICH, S. and KOLTCHINSKII. V. (2001). On inverse problems with unknown operators. IEEE Trans. Inform. Theory 47 2876-2894. MR1872847
    • (2001) IEEE Trans. Inform. Theory , vol.47 , pp. 2876-2894
    • EFROMOVICH, S.1    KOLTCHINSKII, V.2
  • 12
    • 50649114131 scopus 로고    scopus 로고
    • ENGL, H. W., HANKE. M. and NEUBAUER. A. (2000). Regularization of Inverse Problems. Kluwer Academic Press, Dordrecht. MR1408680
    • ENGL, H. W., HANKE. M. and NEUBAUER. A. (2000). Regularization of Inverse Problems. Kluwer Academic Press, Dordrecht. MR1408680
  • 13
    • 33644907163 scopus 로고    scopus 로고
    • Nonparametric methods for inference in the presence of instrumental variables
    • MR2253107
    • HALL, P. and HOROWITZ, J. L. (2005). Nonparametric methods for inference in the presence of instrumental variables. Ann. Statist. 33 2904-2929. MR2253107
    • (2005) Ann. Statist , vol.33 , pp. 2904-2929
    • HALL, P.1    HOROWITZ, J.L.2
  • 14
    • 0346638494 scopus 로고    scopus 로고
    • Thresholding algorithms, maxisets and well-concentrated bases
    • MR1821645
    • KERKYACHARIAN. G. and PICARD, D. (2000). Thresholding algorithms, maxisets and well-concentrated bases. Test 9 283-344. MR1821645
    • (2000) Test , vol.9 , pp. 283-344
    • KERKYACHARIAN, G.1    PICARD, D.2
  • 15
    • 50649109972 scopus 로고    scopus 로고
    • KOROSTELEV, A. and TSYBAKOV, A. B. (1993). Minimax Theory of Image Reconstruction. Springer, New York. MR1226450
    • KOROSTELEV, A. and TSYBAKOV, A. B. (1993). Minimax Theory of Image Reconstruction. Springer, New York. MR1226450
  • 16
    • 50649101409 scopus 로고    scopus 로고
    • NUSSBAUM, M. and PEREVERZEV, S. V. (1999). The degree of ill-posedness in stochastic and deterministic models. Preprint No. 509, Weierstrass Institute (WIAS), Berlin.
    • NUSSBAUM, M. and PEREVERZEV, S. V. (1999). The degree of ill-posedness in stochastic and deterministic models. Preprint No. 509, Weierstrass Institute (WIAS), Berlin.
  • 17
    • 33845679335 scopus 로고    scopus 로고
    • Adaptive estimation for affine stochastic delay differential equations
    • MR2121456
    • REISS, M. (2005). Adaptive estimation for affine stochastic delay differential equations. Bernoulli 11 67-102. MR2121456
    • (2005) Bernoulli , vol.11 , pp. 67-102
    • REISS, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.