Free Access
Issue
ESAIM: PS
Volume 15, 2011
Page(s) 69 - 82
DOI https://doi.org/10.1051/ps/2009005
Published online 05 January 2012
  1. A. Arneodo, E. Bacry, S. Jaffard and J.F. Muzy, Singularity spectrum of multifractal functions involving oscillating singularities. The Journal of Fourier Analysis and Applications 4 (1998) 159–174. [CrossRef] [MathSciNet] [Google Scholar]
  2. A. Arneodo, E. Bacry, S. Jaffard and J.F. Muzy, Oscillating singularities and fractal functions. In Spline functions and the theory of wavelets (Montreal, PQ, 1999) , Amer. Math. Soc. Providence, RI (1999) 315–329. [Google Scholar]
  3. J.M. Aubry and S. Jaffard, Random wavelet series. Comm. Math. Phys. 227 (2002) 483–514. [CrossRef] [MathSciNet] [Google Scholar]
  4. E. Bacry, A. Arneodo, U. Frisch, Y. Gagne and E. Hopfinger, Wavelet analysis of fully developed turbulence data and measurement of scaling exponents. In Turbulence and coherent structures (Grenoble, 1989) , Kluwer Acad. Publ. Dordrecht (1989) 203–215. [Google Scholar]
  5. Z. Chi, Construction of stationary self-similar generalized fields by random wavelet expansion. Probab. Theory Related Fields 121 (2001) 269–300. [CrossRef] [MathSciNet] [Google Scholar]
  6. A. Durand, Random wavelet series based on a tree-indexed Markov chain. Comm. Math. Phys. 283 (2008) 451–477. [CrossRef] [MathSciNet] [Google Scholar]
  7. P. Flandrin, Wavelet analysis and synthesis of fractional Brownian Motion. IEEE Trans. Inform. Theory 38 (1992) 910–917. [CrossRef] [MathSciNet] [Google Scholar]
  8. F. Gamboa and J.-M. Loubes, Bayesian estimation of multifractal wavelet function. Bernoulli (2005) 34–57. [Google Scholar]
  9. F. Gamboa and J.-M. Loubes, Estimation of the parameters of a multifractal wavelet function. Test 16 (2007) 383–407. [CrossRef] [MathSciNet] [Google Scholar]
  10. C. Genovese and L. Wasserman, Rates of convergence for the Gaussian mixture sieve. Ann. Statist. 28 (2000) 1105–1127. [CrossRef] [Google Scholar]
  11. S. Jaffard, On lacunary wavelet series. The Annals of Applied Probability 10 (2000) 313–329. [CrossRef] [MathSciNet] [Google Scholar]
  12. B. Lindsay, The geometry of mixture likelihoods: a general theory. Ann. Statist. 11 (1983) 86–94. [CrossRef] [MathSciNet] [Google Scholar]
  13. G. McLachlan and K. Basford, Mixture models. Inference and applications to clustering. Statistics: Textbooks and Monographs 84. Marcel Dekker, Inc., New York (1988). [Google Scholar]
  14. S.G. Mallat, Multiresolution approximations and wavelet orthonormal bases of L2(r). Transactions of the American Mathematical Society 315 (1989) 69–87. [MathSciNet] [Google Scholar]
  15. D.L. McLeish and C.G. Small, Likelihood methods for the discrimination problem. Biometrika 73 (1986) 397–403. [CrossRef] [Google Scholar]
  16. Y. Meyer, Ondelettes et Opérateurs . Hermann (1990). [Google Scholar]
  17. R.H. Riedi, M.S. Crouse, V.J. Ribeiro and R.G. Baraniuk, A multifractal wavelet model with application to network traffic. Institute of Electrical and Electronics Engineers. Transactions on Information Theory 45 (1999) 992–1018. [CrossRef] [MathSciNet] [Google Scholar]
  18. F. Roueff, Almost sure haussdorff dimensions of graphs of random wavelet series. J. Fourier Analysis and App. 9 (2003). [Google Scholar]
  19. A.R. Swensen, The asymptotic distribution of the likelihood ratio for autoregressive time series with a regression trend. J. Multivariate Anal. 16 (1985) 54–70. [CrossRef] [MathSciNet] [Google Scholar]
  20. S. van de Geer, Rates of convergence for the maximum likelihood estimator in mixture models. J. Nonparametr. Statist. 6 (1996) 293–310. [CrossRef] [MathSciNet] [Google Scholar]
  21. A.W. van der Vaart, Asymptotic statistics . Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge (1998). ISBN 0-521-49603-9; 0-521-78450-6. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.