Data-based optimal smoothing of a wavelet density estimator (Q1381769)
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scientific article; zbMATH DE number 1135905
| Language | Label | Description | Also known as |
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| English | Data-based optimal smoothing of a wavelet density estimator |
scientific article; zbMATH DE number 1135905 |
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Data-based optimal smoothing of a wavelet density estimator (English)
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1 July 1998
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The paper considers the problem of estimating a probability based on a complete random sample, using a wavelet-based orthogonal expansion. Section 2 introduces the concepts of wavelets and a basic wavelet density estimator. Section 3 defines the modifications on the empirical wavelet coefficients to construct the new proposed wavelet density estimator, and develops a method for estimating the optimal smoothing parameters based on a finite random sample. Section 4 contains a numerical experiment supporting the promising performance of the modified estimator, while its asymptotic analysis shows for it optimal rates of convergence.
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over-fitting
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under-fitting
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parameter estimation
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wavelet-based orthogonal expansion
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optimal smoothing
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numerical experiment
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