Displaying similar documents to “Asymptotic expansions of the wavelet transform for large and small values of b .”

Local Asymptotic Normality Property for Lacunar Wavelet Series multifractal model

Jean-Michel Loubes, Davy Paindaveine (2011)

ESAIM: Probability and Statistics

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We consider a lacunar wavelet series function observed with an additive Brownian motion. Such functions are statistically characterized by two parameters. The first parameter governs the lacunarity of the wavelet coefficients while the second one governs its intensity. In this paper, we establish the local and asymptotic normality (LAN) of the model, with respect to this couple of parameters. This enables to prove the optimality of an estimator for the lacunarity parameter, and to build...

Local Asymptotic Normality Property for Lacunar Wavelet Series multifractal model

Jean-Michel Loubes, Davy Paindaveine (2012)

ESAIM: Probability and Statistics

Similarity:

We consider a lacunar wavelet series function observed with an additive Brownian motion. Such functions are statistically characterized by two parameters. The first parameter governs the lacunarity of the wavelet coefficients while the second one governs its intensity. In this paper, we establish the local and asymptotic normality (LAN) of the model, with respect to this couple of parameters. This enables to prove the optimality of an estimator for the lacunarity parameter, and to build...

An extension of distributional wavelet transform

R. Roopkumar (2009)

Colloquium Mathematicae

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We construct a new Boehmian space containing the space 𝓢̃'(ℝⁿ×ℝ₊) and define the extended wavelet transform 𝓦 of a new Boehmian as a tempered Boehmian. In analogy to the distributional wavelet transform, it is proved that the extended wavelet transform is linear, one-to-one, and continuous with respect to δ-convergence as well as Δ-convergence.

Wavelets and prediction in time series

Mošová, Vratislava

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Wavelets (see [2, 3, 4]) are a recent mathematical tool that is applied in signal processing, numerical mathematics and statistics. The wavelet transform allows to follow data in the frequency as well as time domain, to compute efficiently the wavelet coefficients using fast algorithm, to separate approximations from details. Due to these properties, the wavelet transform is suitable for analyzing and forecasting in time series. In this paper, Box-Jenkins models (see [1, 5]) combined...

Wavelet transform for functions with values in UMD spaces

Cornelia Kaiser, Lutz Weis (2008)

Studia Mathematica

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We extend the classical theory of the continuous and discrete wavelet transform to functions with values in UMD spaces. As a by-product we obtain equivalent norms on Bochner spaces in terms of g-functions.