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Volumn 56, Issue 5, 1996, Pages 1424-1444

Statistical inverse estimation in Hilbert scales

Author keywords

Deconvolution; Hilbert scales; Indirect nonparametric regression; Inverse estimation; Regularized inversion; Sobolev scales

Indexed keywords

CODING ERRORS; DIFFERENTIAL EQUATIONS; ESTIMATION; INVERSE PROBLEMS; MATHEMATICAL OPERATORS; REGRESSION ANALYSIS; SIGNAL NOISE MEASUREMENT; SIGNAL PROCESSING; SPURIOUS SIGNAL NOISE;

EID: 0030269038     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139994264476     Document Type: Article
Times cited : (176)

References (26)
  • 3
    • 0000256503 scopus 로고
    • Theoretical aspects of ill-posed problems in statistics
    • R. J. CARROLL, A. C. M. VAN ROOIJ, AND F. H. RUYMGAART (1991), Theoretical aspects of ill-posed problems in statistics, Acta Appl. Math., 24, pp. 113-140.
    • (1991) Acta Appl. Math. , vol.24 , pp. 113-140
    • Carroll, R.J.1    Van Rooij, A.C.M.2    Ruymgaart, F.H.3
  • 4
    • 0003232325 scopus 로고
    • Analyse Harmonique non-Commutative sur Certaines Espaces Homogènes
    • Springer-Verlag, New York
    • R. COIFMAN AND G. WEISS (1971), Analyse Harmonique non-Commutative sur Certaines Espaces Homogènes, Lecture Notes in Math. 242, Springer-Verlag, New York.
    • (1971) Lecture Notes in Math. , vol.242
    • Coifman, R.1    Weiss, G.2
  • 5
    • 0030494512 scopus 로고    scopus 로고
    • Cross-validation for parameter selection in inverse estimation problems
    • to appear
    • A. DEY, B. A. MAIR, AND F. H. RUYMGAART (1996), Cross-validation for parameter selection in inverse estimation problems, Scand. J. Statist., to appear.
    • (1996) Scand. J. Statist.
    • Dey, A.1    Mair, B.A.2    Ruymgaart, F.H.3
  • 8
    • 0002531005 scopus 로고
    • Global behavior of deconvolution kernel estimates
    • J. FAN (1991), Global behavior of deconvolution kernel estimates, Statist. Sinica, 1, pp. 541-551.
    • (1991) Statist. Sinica , vol.1 , pp. 541-551
    • Fan, J.1
  • 11
    • 0001696182 scopus 로고
    • What does the spectral theorem say?
    • P. R. HALMOS (1963), What does the spectral theorem say?, Amer. Math. Monthly, 70, pp. 241-247.
    • (1963) Amer. Math. Monthly , vol.70 , pp. 241-247
    • Halmos, P.R.1
  • 12
    • 0000319983 scopus 로고
    • Speed of estimation in positron emission tomography and related problems
    • I. M. JOHNSTONE AND B. W. SILVERMAN (1990), Speed of estimation in positron emission tomography and related problems, Ann. Statist., 18, pp. 251-280.
    • (1990) Ann. Statist. , vol.18 , pp. 251-280
    • Johnstone, I.M.1    Silverman, B.W.2
  • 13
    • 0001855706 scopus 로고
    • Discretization effects in statistical inverse problems
    • _ (1991), Discretization effects in statistical inverse problems, J. Complexity, 7, pp. 1-34.
    • (1991) J. Complexity , vol.7 , pp. 1-34
  • 16
    • 4243091943 scopus 로고
    • Tikhonov regularization for finitely and infinitely smoothing operators
    • B. A. MAIR (1993), Tikhonov regularization for finitely and infinitely smoothing operators, SIAM J. Math. Anal., 25 (1994), pp. 135-147.
    • (1993) SIAM J. Math. Anal. , vol.25 , pp. 135-147
    • Mair, B.A.1
  • 17
    • 0001504070 scopus 로고
    • On a posteriori parameter choice for Tikhonov regularization in Hilbert scales leading to optimal convergence rates
    • A. NEUBAUER (1988), On a posteriori parameter choice for Tikhonov regularization in Hilbert scales leading to optimal convergence rates, SIAM J. Numer. Anal., 25, pp. 1313-1326.
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 1313-1326
    • Neubauer, A.1
  • 19
    • 0000823716 scopus 로고
    • Convergence rates for regularized solutions of integral equations from discrete noisy data
    • D. NYCHKA AND D. D. COX (1989), Convergence rates for regularized solutions of integral equations from discrete noisy data, Ann. Statist., 17, pp. 556-572.
    • (1989) Ann. Statist. , vol.17 , pp. 556-572
    • Nychka, D.1    Cox, D.D.2
  • 21
    • 0000874622 scopus 로고
    • A unified approach to inversion problems in statistics
    • F. H. RUYMGAART (1993), A unified approach to inversion problems in statistics, Math. Methods Statist., 2, pp. 130-146.
    • (1993) Math. Methods Statist. , vol.2 , pp. 130-146
    • Ruymgaart, F.H.1
  • 22
    • 0000935894 scopus 로고
    • Spline smoothing and optimal rates of convergence in nonparametric regression models
    • P. SPECKMAN (1985), Spline smoothing and optimal rates of convergence in nonparametric regression models, Ann. Statist., 13, pp. 970-983.
    • (1985) Ann. Statist. , vol.13 , pp. 970-983
    • Speckman, P.1
  • 23
    • 0000140399 scopus 로고
    • Numerical methods based on Whittaker cardinal, or sinc functions
    • F. STENGER (1981), Numerical methods based on Whittaker cardinal, or sinc functions, SIAM Rev., 23, pp. 165-224.
    • (1981) SIAM Rev. , vol.23 , pp. 165-224
    • Stenger, F.1
  • 24
    • 0022662417 scopus 로고
    • Optimal choice of a truncation level for the truncated SVD solution of linear first kind integral equations when data are noisy
    • C. R. VOGEL (1986), Optimal choice of a truncation level for the truncated SVD solution of linear first kind integral equations when data are noisy, SIAM J. Numer. Anal., 23, pp. 109-117.
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 109-117
    • Vogel, C.R.1
  • 25
    • 0000544453 scopus 로고
    • Practical approximate solutions to linear operator equations when the data are noisy
    • G. WAHBA (1977), Practical approximate solutions to linear operator equations when the data are noisy, SIAM J. Numer. Anal., 14, pp. 651-667.
    • (1977) SIAM J. Numer. Anal. , vol.14 , pp. 651-667
    • Wahba, G.1
  • 26
    • 0002055609 scopus 로고
    • Fourier methods for estimating mixing densities and distributions
    • C.-H. ZHANG (1990), Fourier methods for estimating mixing densities and distributions, Ann. Statist., 18, pp. 806-831.
    • (1990) Ann. Statist. , vol.18 , pp. 806-831
    • Zhang, C.-H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.