Titlebook: Essential Wavelets for Statistical Applications and Data Analysis; R. Todd Ogden Book 1997 Springer Science+Business Media New York 1997 E

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Wavelet-based Diagnostics,In a real data analysis, an essential component is a thorough graphical study of the data. It is not uncommon for graphical data analysis to turn up some interesting (even vital!) aspect of the data set that might be completely overlooked by applying some canned “black box” statistical inference procedure.

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s Fourier decomposition, and the wavelet representation is presented first in terms of its simplest paradigm, the Haar basis. This piecewise constant Haar system is used to describe the concepts of the multiresolution analysis, and these ideas are generalized to other types of wavelet bases.

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https://doi.org/10.1057/9781137529589the existing techniques in use. Though there are many methods currently in use for these applications, this chapter will focus on only two of them: kernel smoothing and orthogonal series estimation. This background should provide a useful lead-in to a discussion of wavelet methods for function estim

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Contemporary Issues in Sustainable Financeto 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 tr

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Contemporary Issues in Sustainable Financewhere Section 7.1 left off, focusing on the nonparametric regression situation. The ideas described here could also be adapted for use in density estimation or other types of function estimation. To focus attention on the methods described in this chapter, it will be assumed throughout that an ortho