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Wavelets from a Statistical Perspective (Hardcover)
Loot Price: R3,203
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Wavelets from a Statistical Perspective (Hardcover)
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Wavelets from a Statistical Perspective offers a modern, 2nd
generation look on wavelets, far beyond the rigid setting of the
equispaced, dyadic wavelets in the early days. With the methods of
this book, based on the lifting scheme, researchers can set up a
wavelet or another multiresolution analysis adapted to their data,
ranging from images to scattered data or other irregularly spaced
observations. Whereas classical wavelets stand a bit apart from
other nonparametric methods, this book adds a multiscale touch to
your spline, kernel or local polynomial smoothing procedure,
thereby extending its applicability to nonlinear, nonparametric
processing for piecewise smooth data. One of the chapters of the
book constructs B-spline wavelets on nonequispaced knots and
multiscale local polynomial transforms. In another chapter, the
link between wavelets and Fourier analysis, ubiquitous in the
classical approach, is explained, but without being inevitable. In
further chapters the discrete wavelet transform is contrasted with
the continuous version, the nondecimated (or maximal overlap)
transform taking an intermediate position. An important principle
in designing a wavelet analysis through the lifting scheme is
finding the right balance between bias and variance. Bias and
variance also play a crucial role in the nonparametric smoothing in
a wavelet framework, in finding well working thresholds or other
smoothing parameters. The numerous illustrations can be reproduced
with the online available, accompanying software. The software and
the exercises can also be used as a starting point in the further
exploration of the material.
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