Abstract
In Chapters 3, 5, 6 and 7 we discussed techniques to construct functions φ and ψ (father and mother wavelets), such that the wavelet expansion (3.5) holds for any function f in L2(IR). This expansion is a special kind of orthogonal series. It is “special”, since unlike the usual Fourier series, the approximation is both in frequency and space. In this chapter we consider the problem of nonparametric statistical estimation of a function f in L2(IR) by wavelet methods. We study the density estimation and nonparametric regression settings. We also present empirical results of wavelet smoothing.
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© 1998 Springer-Verlag New York, Inc.
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Härdle, W., Kerkyacharian, G., Picard, D., Tsybakov, A. (1998). Statistical estimation using wavelets. In: Wavelets, Approximation, and Statistical Applications. Lecture Notes in Statistics, vol 129. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2222-4_10
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DOI: https://doi.org/10.1007/978-1-4612-2222-4_10
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-98453-7
Online ISBN: 978-1-4612-2222-4
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