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Deconvolution Problems in Nonparametric Statistics (Paperback, 2009 ed.)
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Deconvolution Problems in Nonparametric Statistics (Paperback, 2009 ed.)
Series: Lecture Notes in Statistics, 193
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Deconvolution problems occur in many ?elds of nonparametric
statistics, for example, density estimation based on contaminated
data, nonparametric - gression with errors-in-variables, image and
signal deblurring. During the last two decades, those topics have
received more and more attention. As appli- tions of deconvolution
procedures concern many real-life problems in eco- metrics,
biometrics, medical statistics, image reconstruction, one can
realize an increasing number of applied statisticians who are
interested in nonpa- metric deconvolution methods; on the other
hand, some deep results from Fourier analysis, functional analysis,
and probability theory are required to understand the construction
of deconvolution techniques and their properties so that
deconvolution is also particularly challenging for mathematicians.
Thegeneraldeconvolutionprobleminstatisticscanbedescribedasfollows:
Our goal is estimating a function f while any empirical access is
restricted to some quantity h = f?G = f(x?y)dG(y), (1. 1) that is,
the convolution of f and some probability distribution G.
Therefore, f can be estimated from some observations only
indirectly. The strategy is estimating h ?rst; this means producing
an empirical version h of h and, then, applying a deconvolution
procedure to h to estimate f. In the mathematical context, we have
to invert the convolution operator with G where some reg-
ularization is required to guarantee that h is contained in the
invertibility domain of the convolution operator. The estimator h
has to be chosen with respect to the speci?c statistical
experiment."
General
Imprint: |
Springer-Verlag
|
Country of origin: |
Germany |
Series: |
Lecture Notes in Statistics, 193 |
Release date: |
March 2009 |
First published: |
2009 |
Authors: |
Alexander Meister
|
Dimensions: |
235 x 155 x 12mm (L x W x T) |
Format: |
Paperback
|
Pages: |
210 |
Edition: |
2009 ed. |
ISBN-13: |
978-3-540-87556-7 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Probability & statistics
|
LSN: |
3-540-87556-5 |
Barcode: |
9783540875567 |
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