Choice of smoothing parameters in wavelet series estimators. (English) Zbl 1054.62035
Summary: Wavelets have received considerable interest in denoising since D. L. Donoho and I. M. Johnstone [Biometrika 81, 425–455 (1994; Zbl 0815.62019)] introduced wavelet series estimators. The performance of wavelet series estimators depends on two smoothing parameters- a thresholding starting level \(j_0\) and a threshold \(\delta\). We derive a data criterion to choose two smoothing parameters (\(j_0\) and \(\delta\)) simultaneously in wavelet series estimators.
MSC:
62G07 | Density estimation |
62G05 | Nonparametric estimation |
42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
65T60 | Numerical methods for wavelets |
65C60 | Computational problems in statistics (MSC2010) |
Citations:
Zbl 0815.62019References:
[1] | Abramovich F., Wavelets and Statistics pp pp. 5–14– (1995) |
[2] | Bruce A., Applied Wavelet Analysis with S-Plus (1996) · Zbl 0857.65147 |
[3] | DOI: 10.1093/biomet/81.3.425 · Zbl 0815.62019 · doi:10.1093/biomet/81.3.425 |
[4] | DOI: 10.2307/2291512 · Zbl 0869.62024 · doi:10.2307/2291512 |
[5] | Donoho D., Journal of the Royal Statistical Society, Series B 57 pp 301– (1995) |
[6] | Feller W., An Introduction to Probability Theory and Its Applications (1950) · Zbl 0039.13201 |
[7] | Hall P., Statistica Sinica 6 pp 331– (1996) |
[8] | DOI: 10.1109/34.192463 · Zbl 0709.94650 · doi:10.1109/34.192463 |
[9] | DOI: 10.2307/1390705 · doi:10.2307/1390705 |
[10] | Nason G. P., Wavelets and Statistics pp pp. 261–280– (1995) |
[11] | Lee G. H. Hart J. D. (1998) Choosing a threshold for a Fourier series estimators with applications to testing the no-effect hypothesis (submitted for publication) |
[12] | DOI: 10.1016/0167-9473(95)00041-0 · Zbl 0900.62196 · doi:10.1016/0167-9473(95)00041-0 |
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