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Раздел "Обработка
сигналов и изображений\Wavelet Toolbox"
"Вейвлеты, аппроксимация и статистические приложения" (перевод К.А.Алексеева)
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Список литературы
- Abramovich, F., Benjamini, Y. (1996). Adaptive thresholding of wavelet coefficients, Computational Statistics and Data Analysis 22: 351-361
- Adams, R. (1975). Sobolev Spaces, Academic Press, New York.
- Antoniadis, A. (1994). Smoothing noisy data with tapered coiflet series, Technical Report RR 993-M, University of Grenoble.
- Antoniadis, A., Gregoire, G., McKeague, I. (1994). Wavelet methods for curve estimation, Journal of the American Statistical Association 89: 1340-1353.
- Antoniadis, A, Oppenheim, G. (1995). Wavelets and Statistics, Vol. 103 of Lecture Notes in Statistics, Springer, Heidelberg.
- Assouad, P. (1983). Deux remarques sur l'estimation, Comptes Rendus Acad. Sci.Paris (A) 296: 1021-1024.
- Auscher, P. (1992). Solution of two problems on wavelets, Preprint, IRMAR, Univ. Rennes I.
- Bergh, J., Lofstrom, J. (1976). Interpolation spaces - An Introduction, Springer Verlag, New York.
- Besov, O. V., Iliin, V. L. & Nikolskii, S. M. (1978). Integral Representations of Functions and Embedding Theorems., J. Wiley, New York.
- Beylkin, G., Coifman, R. R. & Rokhlin, V. (1991). Fast wavelet transforms and numerical algorithms, Comm. Pure and Appl. Math. 44: 141-183.
- Birge, L. (1983). Approximation dans les espaces metriques et theorie de l'estimation, Zeitschrift fur Wahrscheinlichkeitstheorie und verwandte Gebiete 65: 181-237.
- Birge, L. & Massart, P. (1997). From model selection to adaptive estimation, in Pollard(ed.), Festschrift for L. Le Cam, Springer, pp. 55-88.
- Black, F. & Scholes, M. (1973). The pricing of options and corporate liabilities, Journal of Political Economy 81: 637-654.
- Bossaerts, P., Hafner, C. & Hardle, W. (1996). Foreign exchange-rates have surprising volatility, in P. Robinson (ed.), Ted Hannan Memorial Volume, Springer Verlag.
- Bretagnolle, J. & Huber, C. (1979). Estimation des densites: risque minimax, Z. Wahrscheinlichkeitstheorie und Verwandte Gebiete 47: 119-137.
- Brown, L.-D. & Low, M. L. (1996). Asymptotic equivalence of non-parametric regression and white noise, Annals of Statistics 24: 2384-2398.
- Bruce, A. & Gao, H.-Y. (1996). Applied Wavelet Analysis with S-Plus, Springer Verlag,Heidelberg, New York.
- Bruce, A. & Gao, H.-Y. (1996). Understanding waveshrink: variance and bias estimation, Biometrika 83: 727-745.
- Burke-Hubbard, B. (1995). Ondes et ondelettes, Pour la science, Paris.
- Centsov, N. N. (1962). Evaluation of an unknown distribution density from observations, Soviet Math. Dokl. 3: 1599-1562.
- Chui, C. (1992). An Introduction to Wavelets, Academic Press, Boston.
- Chui, C. (1992). Wavelets: a Tutorial in Theory and Applications, Academic Press, Boston.
- Cohen, A., Daubechies, I., Vial, P. (1993). Wavelets on the interval and fast wavelet transform, Journal of Applied and Computational Harmonic Analysis 1: 54-81.
- Cohen, A., Ryan, R. (1995). Wavelets and Multiscale Signal Processing, Chapman & Hall.
- Coifman, R. R., Donoho, D. (1995). Translation-invariant de-noising, in Antoniadis & Oppenheim (1995), pp. 125-150.
- Dahlhaus, R. (1997). Fitting time series models to nonstationary processes, Annals of Statistics 25: 1-37.
- Daubechies, I. (1988). Orthonormal bases of compactly supported wavelets, Comm. Pure and Appl. Math. 41: 909-996.
- Daubechies, I. (1992). Ten Lectures on Wavelets, SIAM, Philadelphia.
- Delyon, B., Juditsky, A. (1996). On minimax wavelet estimators, Journal of Applied and Computational Harmonic Analysis 3: 215-228.
- Delyon, B., Juditsky, A. (1996). On the computation of wavelet coefficients, Technical report, IRSA/INRIA, Rennes.
- DeVore, R. A., Lorentz, G. (1993). Constructive Approximation, Springer-Verlag, New York.
- Donoho, D. (1992). De-noising via soft-thresholding, Technical report 409, Dept. of Statistics, Stanford University.
- Donoho, D. (1992). Interpolating wavelet transforms, Technical report 408, Dept. of Statistics, Stanford University.
- Donoho, D. (1993). Smooth wavelet decompositions with blocky coefficient kernels, Technical report, Dept. of Statistics, Stanford University.
- Donoho, D. (1994). Statistical estimation and optimal recovery, Annals of Statistics 22: 238-270.
- Donoho, D. (1995). Nonlinear solutions of linear inverse problems by wavelet-vaguelette decomposition, Journal of Applied and Computational Harmonic Analysis 2: 101-126.
- Donoho, D., Johnstone, I. (1991). Minimax estimation via wavelet shrinkage, Tech. Report, Stanford University.
- Donoho, D. & Johnstone, I. (1994). Ideal spatial adaptation by wavelet shrinkage, Biometrika 81: 425-455.
- Donoho, D. & Johnstone, I. (1994). Minimax risk over -balls for -error, Probabiliy Theory and Related Fields 99: 277-303.
- Donoho, D. & Johnstone, I. (1995). Adapting to unknown smoothness via wavelet shrinkage, Journal of the American Statistical Association 90: 1200-1224.
- Donoho, D. & Johnstone, I. (1996). Neoclassical minimax problems, thresholding and adaptive function estimation, Bernoulli 2: 39-62.
- Donoho, D., Johnstone, I., Kerkyacharian, G. & Picard, D. (1995). Wavelet shrinkage: Asymptopia?, Journal of the Royal Statistical Society, Series B 57: 301-369.
- Donoho, D., Johnstone, I., Kerkyacharian, G. & Picard, D. (1996). Density estimation by wavelet thresholding, Annals of Statistics 24: 508-539.
- Donoho, D., Johnstone, I., Kerkyacharian, G. & Picard, D. (1997). Universal near minimaxity of wavelet shrinkage, in D. Pollard (ed.), Festschrift for L. Le Cam, Springer, N.Y. e.a., pp. 183-218.
- Donoho, D., Mallat, S. G. & von Sachs, R. (1996). Estimating covariances of locally stationary processes: Consistency of best basis methods, Technical report, University of Berkeley.
- Doukhan, P. (1988). Formes de Toeplitz associees a une analyse multiechelle, Comptes Rendus Acad. Sci.Paris (A) 306: 663-666.
- Doukhan, P. & Leon, J. (1990). Deviation quadratique d'estimateurs d'une densite par projection orthogonale, Comptes Rendus Acad. Sci. Paris, (A) 310: 425-430.
- Efroimovich, S. (1985). Nonparametric estimation of a density with unknown moothness, Theory of Probability and its Applications 30: 524-534.
- Efroimovich, S. & Pinsker, M. (1981). Estimation of square-integrable density on the asis of a sequence of observations, Problems of Information Transmission 17: 182-195.
- Fama, E. F. (1976). Foundations of Finance, Basil Blackwell, Oxford.
- Fan, J. (1994). Test of significance based on wavelet thresholding and Neyman's truncation. Preprint.
- Fix, G. & Strang, G. (1969). A Fourier analysis of the finite element method, Stud. Appl. Math. 48: 265-273.
- Foufoula-Georgiou, E. & Kumar, P. (eds) (1994). Wavelets in Geophysics, Academic Press, Boston/London/Sydney.
- Gao, H.-Y. (1993). Choice of thresholds for wavelet estimation of the log spectrum. Preprint 430. Dept. of Stat. Stanford University.
- Gao, H.-Y. (1993). Wavelet estimation of spectral densities in time series analysis. PhD Dissertation. University of California, Berkeley.
- Gasser, T., Stroka, L. & Jennen-Steinmetz, C. (1986). Residual variance and residual pattern in nonlinear regression, Biometrika 73: 625-633.
- Genon-Catalot, V., Laredo, C. & Picard, D. (1992). Nonparametric estimation of the variance of a diffusion by wavelet methods, Scand. Journal of Statistics 19: 319-335.
- Ghysels, E., Gourieroux, C. & Jasiak, J. (1995). Trading patterns, time deformation and stochastic volatility in foreign exchange markets, Discussion paper, CREST, Paris.
- Gourieroux, C. (1992). Modeles ARCH et Applications Financieres, Economica, Paris.
- Hall, P. & Heyde, C. C. (1980). Martingale Limit Theory and its Applications, Acad. Press, New York.
- Hall, P., Kerkyacharian, G. & Picard, D. (1996). Adaptive minimax optimality of block thresholded wavelet estimators, Statistica Sinica. Submitted.
- Hall, P., Kerkyacharian, G. & Picard, D. (1996). Note on the wavelet oracle, Technical report, Aust. Nat. University, Canberra.
- Hall, P., Kerkyacharian, G. & Picard, D. (1996). On block thresholding for curve estimators using kernel and wavelet methods. Submitted.
- Hall, P., McKay, I. & Turlach, B. A. (1996). Performance of wavelet methods for functions with many discontinuities, Annals of Statistics 24: 2462-2476.
- Hall, P. & Patil, P. (1995). Formulae for mean integrated squared error of nonlinear wavelet-based density estimators, Annals of Statistics 23: 905-928.
- Hall, P. & Patil, P. (1995). On wavelet methods for estimating smooth functions, Bernoulli 1: 41-58.
- Hall, P. & Patil, P. (1996). Effect of threshold rules on performance of wavelet-based curve estimators, Statistica Sinica 6: 331-345.
- Hall, P. & Patil, P. (1996). On the choice of smoothing parameter, threshold and truncation in nonparametric regression by nonlinear wavelet methods, Journal of the Royal Statistical Society, Series B 58: 361-377.
- Hall, P. & Turlach, B. A. (1995). Interpolation methods for nonlinear wavelet regression with irregularly spaced design. Preprint.
- Hardle, W. (1990). Applied Nonparametric Regression, Cambridge University Press, Cambridge.
- Hardle, W., Klinke, S. & Turlach, B. A. (1995). XploRe - an Interactive Statistical Computing Environment, Springer, Heidelberg.
- Hardle, W. & Scott, D. W. (1992). Smoothing by weighted averaging of rounded points, Computational Statistics 7: 97-128.
- Hildenbrand, W. (1994). Market Demand, Princeton University Press, Princeton.
- Hoffmann, M. (1996). Methodes adaptatives pour l'estimation non-parametrique des coefficients d'une diffusion, Phd thesis, Universite Paris VII.
- Holschneider, M. (1995). Wavelets: an Analysis Tool, Oxford University Press, Oxford.
- Ibragimov, I. A. & Hasminskii, R. Z. (1980). On nonparametric estimation of regression, Soviet Math. Dokl. 21: 810-814.
- Ibragimov, I. A. & Hasminskii, R. Z. (1981). Statistical Estimation: Asymptotic Theory, Springer, New York.
- Johnstone, I. (1994). Minimax Bayes, asymptotic minimax and sparse wavelet priors, in S.Gupta & J.Berger (eds), Statistical Decision Theory and Related Topics, Springer, pp. 303-326.
- Johnstone, I., Kerkyacharian, G. & Picard, D. (1992). Estimation d'une densite de probabilite par methode d'ondelette, Comptes Rendus Acad. Sci. Paris, (1) 315: 211-216.
- Johnstone, I. & Silverman, B. W. (1997). Wavelet methods for data with correlated noise, Journal of the Royal Statistical Society, Series B 59: 319-351.
- Juditsky, A. (1997). Wavelet estimators: adapting to unknown smoothness, Mathematical Methods of Statistics 6: 1-25.
- Kahane, J. P. & Lemarie-Rieusset, P. (1995). Fourier Series and Wavelets, Gordon and Breach Science Publishers, Amsterdam.
- Kaiser, G. (1995). A Friendly Guide to Wavelets, Birkhauser, Basel.
- Katznelson, Y. (1976). An Introduction to Harmonic Analysis, Dover, New York.
- Kerkyacharian, G. & Picard, D. (1992). Density estimation in Besov spaces, Statistics and Probability Letters 13: 15-24.
- Kerkyacharian, G. & Picard, D. (1993). Density estimation by kernel and wavelet methods: optimality of Besov spaces, Statistics and Probability Letters 18: 327-336.
- Kerkyacharian, G., Picard, D. & Tribouley, K. (1996). Adaptive density estimation, Bernoulli 2: 229-247.
- Korostelev, A. P. & Tsybakov, A. B. (1993). Estimation of the density support and its functionals, Problems of Information Transmission 29: 1-15.
- Korostelev, A. P. & Tsybakov, A. B. (1993). Minimax Theory of Image Reconstruction, Springer, New York.
- Leadbetter, M. R., Lindgren, G. & Rootzen, H. (1986). Extremes and Related Properties of Random Sequences and Processes, Springer, N.Y.
- Ledoux, M. & Talagrand, M. (1991). Probability in Banach Spaces, Springer, New York.
- Lemarie, P. (1991). Fonctions a support compact dans les analyses multi-resolutions, Revista Mat. Iberoamericana 7: 157-182.
- Lemarie-Rieusset, P. (1993). Ondelettes generalisees et fonctions d'echelle a support compact, Revista Mat. Iberoamericana 9: 333-371.
- Lemarie-Rieusset, P. (1994). Projecteurs invariants, matrices de dilatation, ondelettes et analyses multi-resolutions, Revista Mat. Iberoamericana 10: 283-347.
- Lepski, O., Mammen, E. & Spokoiny, V. (1997). Optimal spatial adaptation to inhomogeneous smoothness: an approach based on kernel estimates with variable bandwidth selectors, Annals of Statistics 25: 929-947.
- Lepski, O. & Spokoiny, V. (1995). Local adaptation to inhomogeneous smoothness: resolution level, Mathematical Methods of Statistics 4: 239-258.
- Lepskii, O. (1990). On a problem of adaptive estimation in gaussian white noise, Theory Prob. Appl. 35: 454-466.
- Lepskii, O. (1991). Asymptotically minimax adaptive estimation I: Upper bounds. Optimal adaptive estimates, Theory Prob. Appl. 36: 682-697.
- Lepskii, O. (1992). Asymptotically minimax adaptive estimation II: Statistical models without optimal adaptation. Adaptive estimates, Theory Prob. Appl. 37: 433-468.
- Lintner, J. (1965). Security prices, risk and maximal gains from diversification, Journal of Finance 20: 587-615.
- Mallat, S. G. (1989). A theory for multiresolution signal decomposition: the wavelet representation, IEEE Transactions on Pattern Analysis and Machine Intelligence 11: 674-693.
- Marron, J. S., Adak, S., Johnstone, I., Neumann, M. & Patil, P. (1995). Exact risk analysis of wavelet regression. Manuscript.
- Marron, J. S. & Tsybakov, A. B. (1995). Visual error criteria for qualitative smoothing, Journal of the American Statistical Association 90: 499-507.
- Meyer, Y. (1990). Ondelettes et operateurs, Hermann, Paris.
- Meyer, Y. (1991). Ondelettes sur l'intervalle, Rev. Mat. Iberoamericana 7: 115-133.
- Meyer, Y. (1993). Wavelets: Algorithms and Applications, SIAM, Philadelphia.
- Misiti, M., Misiti, Y., Oppenheim, G. & Poggi, J. (1996). Wavelet TOOLBOX, The MathWorks Inc., Natick, MA.
- Moulin, P. (1993). Wavelet thresholding techniques for power spectrum estimation, IEEE. Trans. Signal Processing 42: 3126-3136.
- Nason, G. (1996). Wavelet shrinkage using cross-validation, Journal of the Royal Statistical Society, Series B 58: 463-479.
- Nason, G. & Silverman, B. W. (1994). The discrete wavelet transform in S, Journal of Computational and Graphical Statistics 3: 163-191.
- Nemirovskii, A. S. (1986). Nonparametric estimation of smooth regression functions, Journal of Computer and System Sciences 23(6): 1-11.
- Nemirovskii, A. S., Polyak, B. T. & Tsybakov, A. B. (1983). Estimators of maximum likelihood type for nonparametric regression, Soviet Math. Dokl. 28: 788-92.
- Nemirovskii, A. S., Polyak, B. T. & Tsybakov, A. B. (1985). Rate of convergence of nonparametric estimators of maximum likelihood type, Problems of Information Transmission 21: 258-272.
- Neumann, M. (1996). Multivariate wavelet thresholding: a remedy against the curse of dimensionality? Preprint 239. Weierstrass Inst. of Applied Analysis and Stochastics, Berlin.
- Neumann, M. (1996). Spectral density estimation via nonlinear wavelet methods for stationary non-gaussian time series, Journal of Time Series Analysis 17: 601-633.
- Neumann, M. & Spokoiny, V. (1995). On the efficiency of wavelet estimators under arbitrary error distributions, Mathematical Methods of Statistics 4: 137-166.
- Neumann, M. & von Sachs, R. (1995). Wavelet thresholding: beyond the Gaussian iid situation, in Antoniadis & Oppenheim (1995), pp. 301-329.
- Neumann, M. & von Sachs, R. (1997). Wavelet thresholding in anisotropic function classes and application to adaptive estimation of evolutionary spectra, Annals of Statistics 25: 38-76.
- Nikolskii, S. M. (1975). Approximation of Functions of Several Variables and Imbedding Theorems, Springer, New York.
- Nussbaum, M. (1985). Spline smoothing in regression models and asymptotic efficiency, Annals of Statistics 13: 984-97.
- Nussbaum, M. (1996). Asymptotic equivalence of density estimation and gaussian white noise, Annals of Statistics 24: 2399-2430.
- Ogden, T. (1997). Essential Wavelets for Statistical Applications and Data Analysis, Birkhauser, Basel.
- Ogden, T. & Parzen, E. (1996). Data dependent wavelet thresholding in nonparametric regression with change point applications, Computational Statistics and Data Analysis 22: 53-70.
- Oppenheim, A. & Schafer, R. (1975). Digital Signal Processing, Prentice-Hall, New York.
- Papoulis, G. (1977). Signal Analysis, McGraw Hill.
- Park, B. V. & Turlach, B. A. (1992). Practical performance of several data driven bandwidth selectors, Computational Statistics 7: 251-270.
- Peetre, J. (1975). New thoughts on Besov spaces, vol. 1, Technical report, Duke University, Durham, NC.
- Pesquet, J. C., Krim, H. & Carfantan, H. (1994). Time invariant orthogonal wavelet representation. Submitted for publication.
- Petrov, V. V. (1995). Limit Theorems of Probability Theory, Clarendon Press, Oxford.
- Pinsker, M. (1980). Optimal filtering of square integrable signals in gaussian white noise, Problems of Information Transmission 16: 120-133.
- Pollard, D. (1984). Convergence of Stochastic Processes, Springer, New York.
- Raimondo, M. (1996). Modelles en ruptures, Phd thesis, Universite Paris VII.
- Rioul, O. & Vetterli, M. (1991). Wavelets and signal processing, IEEE Signal Processing Magazine 8(4): 14-38.
- Rosenthal, H. P. (1970). On the subspaces of spanned by sequences of independent random variables, Israel Journal of Mathematics 8: 273-303.
- Sharpe, W. (1964). Capital asset prices: a theory of market equilibrium under conditions of risk, Journal of Finance 19: 425-442.
- Silverman, B. W. (1986). Density Estimation for Statistics and Data Analysis, Chapman and Hall, London.
- Spokoiny, V. (1996). Adaptive hypothesis testing using wavelets, Annals of Statistics 25: 2477-2498.
- Stein, C. M. (1981). Estimation of the mean of a multivariate normal distribution, Annals of Statistics 9: 1135-1151.
- Stein, E. & Weiss, G. (1971). Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton.
- Stone, C. J. (1980). Optimal rates of convergence for nonparametric estimators, Annals of Statistics 8: 1348-60.
- Stone, C. J. (1982). Optimal global rates of convergence for nonparametric regression, Annals of Statistics 10: 1040-1053.
- Strang, G. & Nguyen, T. (1996). Wavelets and Filter Banks, Wellesley-Cambridge Press, Wellesley, MA.
- Tribouley, K. (1995). Practical estimation of multivariate densities using wavelet methods, Statistica Neerlandica 49: 41-62.
- Tribouley, K. & Viennet, G. (1998). Adaptive estimation of the density in a –mixing framework., Ann. de l'Institut H. Poincare, to appear.
- Triebel, H. (1992). Theory of Function Spaces II, Birkhauser Verlag, Basel.
- Tsybakov, A. B. (1995). Pointwise and sup-norm adaptive signal estimation on the Sobolev classes. Submitted for publication.
- von Sachs, R. & Schneider, K. (1996). Wavelet smoothing of evolutionary spectra by non-linear thresholding, Journal of Applied and Computational Harmonic Analysis: 268-282.
- Wang, Y. (1995). Jump and sharp cusp detection by wavelets, Biometrika 82: 385-397.
- Wang, Y. (1996). Function estimation via wavelet shrinkage for long-memory data, Annals of Statistics 24: 466-484.
- Young, R. K. (1993). Wavelet Theory and its Applications, Kluwer Academic Publishers, Boston/Dordrecht/London.
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