A note on the wavelet oracle
Identifieur interne : 00C462 ( Main/Exploration ); précédent : 00C461; suivant : 00C463A note on the wavelet oracle
Auteurs : Peter Hall [Australie] ; Gérard Kerkyacharian [Australie, France] ; Dominique Picard [Australie, France]Source :
- Statistics and Probability Letters [ 0167-7152 ] ; 1999.
Descripteurs français
- Pascal (Inist)
English descriptors
- KwdEn :
- Block thresholding, Cient, Convergence rate, Donoho, Elsevier science, Empirical wavelet expansion, Estimator, Individual functions, Logarithmic factor, Nonparametric regression, Optimal rate, Optimization method, Oracle, Previous paragraph, Same performance, Statistics probability letters, Target function, Thresholding, Unknown smoothness, Variance, Variance analysis, Wavelet, Wavelet expansion, Wavelet methods, Wavelet shrinkage, Wavelet transformation.
- Teeft :
- Block thresholding, Cient, Convergence rate, Donoho, Elsevier science, Empirical wavelet expansion, Estimator, Individual functions, Logarithmic factor, Nonparametric regression, Optimal rate, Oracle, Previous paragraph, Same performance, Statistics probability letters, Target function, Thresholding, Unknown smoothness, Variance, Wavelet, Wavelet expansion, Wavelet methods, Wavelet shrinkage.
Abstract
Abstract: The extent to which wavelet function estimators achieve benchmark levels of performance is sometimes described in terms of our ability to interpret a mythical oracle, who has access to the “truth” about the target function. Since he is so wise, he is able to threshold in an optimal manner – that is, to include a term in the empirical wavelet expansion if and only if the square of the corresponding true coefficient is larger than the variance of its estimate. In this note we show that if thresholding is performed in blocks then, for piecewise-smooth functions, we can achieve the same first-order mean-square performance as the oracle, right down to the constant factor, for fixed, piecewise-smooth functions.
Url:
DOI: 10.1016/S0167-7152(98)00282-X
Affiliations:
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Le document en format XML
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<front><div type="abstract" xml:lang="en">Abstract: The extent to which wavelet function estimators achieve benchmark levels of performance is sometimes described in terms of our ability to interpret a mythical oracle, who has access to the “truth” about the target function. Since he is so wise, he is able to threshold in an optimal manner – that is, to include a term in the empirical wavelet expansion if and only if the square of the corresponding true coefficient is larger than the variance of its estimate. In this note we show that if thresholding is performed in blocks then, for piecewise-smooth functions, we can achieve the same first-order mean-square performance as the oracle, right down to the constant factor, for fixed, piecewise-smooth functions.</div>
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