Displaying similar documents to “Adaptive wavelet estimation of a biased density for strongly mixing sequences.”

On the adaptive wavelet estimation of a multidimensional regression function under α -mixing dependence: Beyond the standard assumptions on the noise

Christophe Chesneau (2013)

Commentationes Mathematicae Universitatis Carolinae

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We investigate the estimation of a multidimensional regression function f from n observations of an α -mixing process ( Y , X ) , where Y = f ( X ) + ξ , X represents the design and ξ the noise. We concentrate on wavelet methods. In most papers considering this problem, either the proposed wavelet estimator is not adaptive (i.e., it depends on the knowledge of the smoothness of f in its construction) or it is supposed that ξ is bounded or/and has a known distribution. In this paper, we go far beyond this classical...

Stein estimation for infinitely divisible laws

R. Averkamp, C. Houdré (2006)

ESAIM: Probability and Statistics

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Unbiased risk estimation, à la Stein, is studied for infinitely divisible laws with finite second moment.

A scale-space approach with wavelets to singularity estimation

Jérémie Bigot (2005)

ESAIM: Probability and Statistics

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This paper is concerned with the problem of determining the typical features of a curve when it is observed with noise. It has been shown that one can characterize the Lipschitz singularities of a signal by following the propagation across scales of the modulus maxima of its continuous wavelet transform. A nonparametric approach, based on appropriate thresholding of the empirical wavelet coefficients, is proposed to estimate the wavelet maxima of a signal observed with noise at various...

Adaptive estimation of a quadratic functional of a density by model selection

Béatrice Laurent (2005)

ESAIM: Probability and Statistics

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We consider the problem of estimating the integral of the square of a density f from the observation of a n sample. Our method to estimate ∫ ℝ f 2 ( x ) d x is based on model selection via some penalized criterion. We prove that our estimator achieves the adaptive rates established by Efroimovich and Low on classes of smooth functions. A key point of the proof is an exponential inequality for U -statistics of order 2 due to Houdré and Reynaud.

Daubechies wavelets on intervals with application to BVPs

Václav Finěk (2004)

Applications of Mathematics

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In this paper, Daubechies wavelets on intervals are investigated. An analytic technique for evaluating various types of integrals containing the scaling functions is proposed; they are compared with classical techniques. Finally, these results are applied to two-point boundary value problems.