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Volumn 24, Issue 2, 1996, Pages 466-484

Function estimation via wavelet shrinkage for long-memory data

Author keywords

Cross validation; Fractional Brownian motion; Fractional Gaussian noise; Fractional Gaussian noise model; Long range dependence; Minimax risk; Nonparametric regression; Threshold; Vaguelette; Wavelet; Wavelet vaguelette decomposition

Indexed keywords


EID: 0030492140     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1032894449     Document Type: Article
Times cited : (86)

References (39)
  • 1
    • 0024078858 scopus 로고
    • Signal detection in fractional Gaussian noise
    • BARTON, R. J. and POOR, H. V. (1988). Signal detection in fractional Gaussian noise. IEEE Trans. Inform. Theory 34 943-959.
    • (1988) IEEE Trans. Inform. Theory , vol.34 , pp. 943-959
    • Barton, R.J.1    Poor, H.V.2
  • 2
    • 85013519631 scopus 로고
    • Wavelet decomposition of one and several dimensional Gaussian processes
    • (L. L. Schumaker and G. Webb, eds.) Academic, New York
    • BENASSI, A. and JAFFARD, S. (1993). Wavelet decomposition of one and several dimensional Gaussian processes. In Recent Advances in Wavelet Analysis (L. L. Schumaker and G. Webb, eds.) 119-154. Academic, New York.
    • (1993) Recent Advances in Wavelet Analysis , pp. 119-154
    • Benassi, A.1    Jaffard, S.2
  • 3
    • 84972520545 scopus 로고
    • Long-range dependence
    • with discussion
    • BERAN, J. (1992). Long-range dependence (with discussion). Statist. Sci. 7 404-427.
    • (1992) Statist. Sci. , vol.7 , pp. 404-427
    • Beran, J.1
  • 5
    • 0030335402 scopus 로고    scopus 로고
    • Asymptotic equivalence of nonparametric regression and white noise
    • To appear
    • BROWN, L. and LOW, M. (1996). Asymptotic equivalence of nonparametric regression and white noise. Ann. Statist. To appear.
    • (1996) Ann. Statist.
    • Brown, L.1    Low, M.2
  • 9
    • 85013565266 scopus 로고
    • Two recent results on wavelets: Wavelet bases for the interval, and biorthogonal wavelet diagonalizing the derivative operator
    • (L. L. Schumaker and G. Webb, eds.) Academic, New York
    • DAUBECHIES, I. (1994). Two recent results on wavelets: wavelet bases for the interval, and biorthogonal wavelet diagonalizing the derivative operator. In Recent Advances in Wavelet Analysis (L. L. Schumaker and G. Webb, eds.) 237-257. Academic, New York.
    • (1994) Recent Advances in Wavelet Analysis , pp. 237-257
    • Daubechies, I.1
  • 10
    • 0000370306 scopus 로고
    • Nonlinear wavelet methods for recovery of signals, densities, and spectra from indirect and noisy data
    • (I. Daubechies, ed.) Amer. Math. Soc., Providence, RI
    • DONOHO, D. L. (1993). Nonlinear wavelet methods for recovery of signals, densities, and spectra from indirect and noisy data. In Different Perspectives on Wavelet (I. Daubechies, ed.) 173-205. Amer. Math. Soc., Providence, RI.
    • (1993) Different Perspectives on Wavelet , pp. 173-205
    • Donoho, D.L.1
  • 11
    • 0029288068 scopus 로고
    • Nonlinear solutions of linear inverse problems by wavelet-vaguelette decomposition
    • DONOHO, D. L. (1995). Nonlinear solutions of linear inverse problems by wavelet-vaguelette decomposition. Appl. Comput. Harmon. Anal. 2 101-126.
    • (1995) Appl. Comput. Harmon. Anal. , vol.2 , pp. 101-126
    • Donoho, D.L.1
  • 12
    • 0041958932 scopus 로고
    • Ideal spatial adaptation by wavelet shrinkage
    • DONOHO, D. L. and JOHNSTONE, I. M. (1994). Ideal spatial adaptation by wavelet shrinkage. Biometrika 81 425-455.
    • (1994) Biometrika , vol.81 , pp. 425-455
    • Donoho, D.L.1    Johnstone, I.M.2
  • 14
    • 84950459514 scopus 로고
    • Adapting to unknown smoothness via wavelet shrinking
    • DONOHO, D. L. and JOHNSTONE, I. M. (1995b). Adapting to unknown smoothness via wavelet shrinking. J. Amer. Statist. Assoc. 90 1200-1224.
    • (1995) J. Amer. Statist. Assoc. , vol.90 , pp. 1200-1224
    • Donoho, D.L.1    Johnstone, I.M.2
  • 17
    • 0001573354 scopus 로고
    • Renormalization exponents and optimal pointwise rates of convergence
    • DONOHO, D. L. and LOW, M. G. (1992). Renormalization exponents and optimal pointwise rates of convergence. Ann. Statist. 20 944-970.
    • (1992) Ann. Statist. , vol.20 , pp. 944-970
    • Donoho, D.L.1    Low, M.G.2
  • 18
    • 34250842720 scopus 로고
    • On the spectrum of fractional Brownian motion
    • FLANDRIN, P. (1989). On the spectrum of fractional Brownian motion. IEEE Trans. Inform. Theory 35 197-199.
    • (1989) IEEE Trans. Inform. Theory , vol.35 , pp. 197-199
    • Flandrin, P.1
  • 19
    • 0026628466 scopus 로고
    • Wavelet analysis and synthesis of fractional Brownian motion
    • FLANDRIN, P. (1992). Wavelet analysis and synthesis of fractional Brownian motion. IEEE Trans. Inform. Theory 38 910-917.
    • (1992) IEEE Trans. Inform. Theory , vol.38 , pp. 910-917
    • Flandrin, P.1
  • 20
    • 0001485314 scopus 로고
    • Nonparametric regression with long-range dependence
    • HALL, P. and HART, J. D. (1990a). Nonparametric regression with long-range dependence. Stochastic Process. Appl. 36 339-351.
    • (1990) Stochastic Process. Appl. , vol.36 , pp. 339-351
    • Hall, P.1    Hart, J.D.2
  • 21
    • 0000048014 scopus 로고
    • Convergence rates in density estimation for data from infinite-order moving average processes
    • HALL, P. and HART, J. D. (1990b). Convergence rates in density estimation for data from infinite-order moving average processes. Probab. Theory Related Fields 87 253-274.
    • (1990) Probab. Theory Related Fields , vol.87 , pp. 253-274
    • Hall, P.1    Hart, J.D.2
  • 22
    • 0000272104 scopus 로고
    • Data-driven bandwidth choice for density estimation based on dependent data
    • HART, J. D. and VIEU, P. (1990). Data-driven bandwidth choice for density estimation based on dependent data. Ann. Statist. 18 873-890.
    • (1990) Ann. Statist. , vol.18 , pp. 873-890
    • Hart, J.D.1    Vieu, P.2
  • 24
    • 0020102486 scopus 로고
    • 1/f noise
    • KESHNER, M. S. (1982). 1/f noise. Proc. IEEE 70 212-218.
    • (1982) Proc. IEEE , vol.70 , pp. 212-218
    • Keshner, M.S.1
  • 26
    • 0024700097 scopus 로고
    • A theory for multiresolution signal decomposition: The wavelet representation
    • MALLAT, (1989). A theory for multiresolution signal decomposition: the wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence 11 674-693.
    • (1989) IEEE Transactions on Pattern Analysis and Machine Intelligence , vol.11 , pp. 674-693
  • 27
    • 0000501589 scopus 로고
    • Fractional Brownian motions, fractional noises and applications
    • MANDELBROT, B. B. and VAN NESS, J. W. (1968). Fractional Brownian motions, fractional noises and applications. SIAM Rev. 10 422-437.
    • (1968) SIAM Rev. , vol.10 , pp. 422-437
    • Mandelbrot, B.B.1    Van Ness, J.W.2
  • 29
    • 84944495957 scopus 로고
    • Computer experiments with fractional Gaussian noises
    • MANDELBROT, B. B. and WALLIS, J. R. (1969). Computer experiments with fractional Gaussian noises. Water Resource Research 5 228-267.
    • (1969) Water Resource Research , vol.5 , pp. 228-267
    • Mandelbrot, B.B.1    Wallis, J.R.2
  • 31
    • 0000674772 scopus 로고    scopus 로고
    • Wavelet shrinkage using cross-validation
    • NASON, G. P. (1996). Wavelet shrinkage using cross-validation. J. Roy. Statist. Soc. Ser. B. 58 463-479.
    • (1996) J. Roy. Statist. Soc. Ser. B. , vol.58 , pp. 463-479
    • Nason, G.P.1
  • 32
    • 0026190345 scopus 로고
    • On the wavelet transform of fractional Brownian motion
    • RAMANATHAN, J. and ZEITOUNI, O. (1991). On the wavelet transform of fractional Brownian motion. IEEE Trans. Inform. Theory 37 1156-1158.
    • (1991) IEEE Trans. Inform. Theory , vol.37 , pp. 1156-1158
    • Ramanathan, J.1    Zeitouni, O.2
  • 33
    • 34250409798 scopus 로고
    • Weak convergence to fractional Brownian motion and to the Rosenblatt process
    • TAQQU, M. S. (1975). Weak convergence to fractional Brownian motion and to the Rosenblatt process. Z. Wahrsch. Verw. Gebiete 31 287-302.
    • (1975) Z. Wahrsch. Verw. Gebiete , vol.31 , pp. 287-302
    • Taqqu, M.S.1
  • 34
    • 0026679673 scopus 로고
    • Correlation structure of the discrete wavelet coefficients of fractional Brownian motion
    • TEWFIK, A. H. and KIM, M. (1992). Correlation structure of the discrete wavelet coefficients of fractional Brownian motion. IEEE Trans. Inform. Theory 38 904-909.
    • (1992) IEEE Trans. Inform. Theory , vol.38 , pp. 904-909
    • Tewfik, A.H.1
  • 36
    • 0000999642 scopus 로고
    • Jump and sharp cusp detection by wavelets
    • WANG, Y. (1995a). Jump and sharp cusp detection by wavelets. Biometrika 82 385-397.
    • (1995) Biometrika , vol.82 , pp. 385-397
    • Wang, Y.1
  • 38
    • 0025462413 scopus 로고
    • A Karhunen-Loève-like expansion for 1/f processes via wavelets
    • WORNELL, G. W. (1990). A Karhunen-Loève-like expansion for 1/f processes via wavelets. IEEE Trans. Inform. Theory 36 859-861.
    • (1990) IEEE Trans. Inform. Theory , vol.36 , pp. 859-861
    • Wornell, G.W.1
  • 39
    • 0026829738 scopus 로고
    • Estimation of fractal signals from noisy measurements using wavelets
    • WORNELL, G. W. and OPPENHEIM, A. V. (1992). Estimation of fractal signals from noisy measurements using wavelets. IEEE Transactions on Signal Processing 40 611-623.
    • (1992) IEEE Transactions on Signal Processing , vol.40 , pp. 611-623
    • Wornell, G.W.1    Oppenheim, A.V.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.