Local Asymptotic Normality Property for Lacunar Wavelet Series multifractal model*
Jean-Michel Loubes; Davy Paindaveine
ESAIM: Probability and Statistics (2012)
- Volume: 15, page 69-82
- ISSN: 1292-8100
Access Full Article
topAbstract
topHow to cite
topReferences
top- 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.
- 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.
- J.M. Aubry and S. Jaffard, Random wavelet series. Comm. Math. Phys.227 (2002) 483–514.
- 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.
- Z. Chi, Construction of stationary self-similar generalized fields by random wavelet expansion. Probab. Theory Related Fields121 (2001) 269–300.
- A. Durand, Random wavelet series based on a tree-indexed Markov chain. Comm. Math. Phys.283 (2008) 451–477.
- P. Flandrin, Wavelet analysis and synthesis of fractional Brownian Motion. IEEE Trans. Inform. Theory38 (1992) 910–917.
- F. Gamboa and J.-M. Loubes, Bayesian estimation of multifractal wavelet function. Bernoulli (2005) 34–57.
- F. Gamboa and J.-M. Loubes, Estimation of the parameters of a multifractal wavelet function. Test16 (2007) 383–407.
- C. Genovese and L. Wasserman, Rates of convergence for the Gaussian mixture sieve. Ann. Statist.28 (2000) 1105–1127.
- S. Jaffard, On lacunary wavelet series. The Annals of Applied Probability10 (2000) 313–329.
- B. Lindsay, The geometry of mixture likelihoods: a general theory. Ann. Statist.11 (1983) 86–94.
- G. McLachlan and K. Basford, Mixture models. Inference and applications to clustering. Statistics: Textbooks and Monographs84. Marcel Dekker, Inc., New York (1988).
- S.G. Mallat, Multiresolution approximations and wavelet orthonormal bases of L2(r). Transactions of the American Mathematical Society315 (1989) 69–87.
- D.L. McLeish and C.G. Small, Likelihood methods for the discrimination problem. Biometrika 73 (1986) 397–403.
- Y. Meyer, Ondelettes et Opérateurs . Hermann (1990).
- 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.
- F. Roueff, Almost sure haussdorff dimensions of graphs of random wavelet series. J. Fourier Analysis and App.9 (2003).
- 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.
- S. van de Geer, Rates of convergence for the maximum likelihood estimator in mixture models. J. Nonparametr. Statist.6 (1996) 293–310.
- 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.