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## ‣ On the usefulness of Meyer wavelets for deconvolution and density estimation

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Mathematics - Statistics Theory#Mathematics - Functional Analysis#Statistics - Methodology#62G07#42C40, 41A29

The aim of this paper is to show the usefulness of Meyer wavelets for the
classical problem of density estimation and for density deconvolution from
noisy observations. By using such wavelets, the computation of the empirical
wavelet coefficients relies on the fast Fourier transform of the data and on
the fact that Meyer wavelets are band-limited functions. This makes such
estimators very simple to compute and this avoids the problem of evaluating
wavelets at non-dyadic points which is the main drawback of classical
wavelet-based density estimators. Our approach is based on term-by-term
thresholding of the empirical wavelet coefficients with random thresholds
depending on an estimation of the variance of each coefficient. Such estimators
are shown to achieve the same performances of an oracle estimator up to a
logarithmic term. These estimators also achieve near-minimax rates of
convergence over a large class of Besov spaces. A simulation study is proposed
to show the good finite sample performances of the estimator for both problems
of direct density estimation and density deconvolution.

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