With a basic understanding of wavelet theory and a knowledge of the practical issues involved in applying wavelets to observed data, we are now ready to extend the basic methods of Chapter 3 to more sophisticated techniques on a wide variety of applications. Perhaps the most common wavelet application in statistics is nonparametric regression, which is covered in some depth in Section 7.1. This will serve as a groundwork for other applications treated later in this chapter: density estimation, estimation of the spectral density in time series, and the general change-point problem. Extensions of these methods will be given in the context of nonparametric regression in Chapter 8.
KeywordsSpectral Density Wavelet Coefficient Nonparametric Regression Spectral Density Function Hard Thresholding
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