Abstract
Wavelets are a powerful statistical tool which can be used for a wide range of applications, namely
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describing a signal, nonparametic estimation
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parsimonious (approximate) representation, data compression
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smoothing and image denoising
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jump detection and test procedures.
One of the main advantages of wavelets is that they offer a simultaneous localization in time and frequency domain. The second main advantage of wavelets is that, using fast wavelet transform, it is computationally very fast.
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Bibliography
Coifman, R. R. and Donoho, D. (1995). Translation-invariant denoising, in Antoniadis and Oppenheim:Wavelets and Statistics, Lecture Notes in Statistics 103: 125 – 150.
Daubechies, I. (1988). Orthonormal bases of compactly supported wavelets,Comm. Pure and Appl. Math. 41: 909 – 996.
Daubechies, I. (1992).Ten Lectures on Wavelets, SIAM, Philadelphia.
Donoho, D. and Johnstone, I. (1995). Adapting to unknown smoothness via wavelet shrinkage,Journal of the American Statistical Association 90: 1200 – 1224.
Donoho, D. and Johnstone, I. (1998). Minimax estimation via wavelet shrinkage,Annals of Statistics 26: 879 – 921.
Härdle, W., Kerkyacharian, G., Picard, D. and Tsybakov, A. (1998).Wavelets, Approximation, and Statistical Applications, Lecture Notes in Statistics 129, Springer Verlag, New York.
Kaiser, G. (1995).A Friendly Guide to Wavelets, Birkhäuser, Basel
Nason, G. and Silverman, B. W. (1994). The discrete wavelet transform in S,Journal of Computer and System Science 3: 163 – 191.
Neumann, M. (1996). Spectral density estimation via nonlinear wavelet methods for stationary non-gaussian time series,Journal of Time Series Analysis 17: 601 – 633.
Neumann, M. (1996).Multivariate wavelet thresholding: a remedy against the curse of dimensionalityDiscussion Paper 42, SFB 373, Humboldt- Universitat zu Berlin, Germany
Neumann, M. and Sachs, R. (1997). Wavelet thresholding in anisotropic function classes and application to adaptive estimation of evolutionary spectra,Annals of Statistics25: 38 – 76.
Stein, C. M. (1981). Estimation of the mean of a multivariate normal distribution,Annals of Statistics 9 1135–1151.
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Golubev, Y., Härdle, W., Hlávka, Z., Klinke, S., Neumann, M.H., Sperlich, S. (2000). Wavelets. In: XploRe — Learning Guide. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60232-0_14
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DOI: https://doi.org/10.1007/978-3-642-60232-0_14
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