Deconvolution Problems in Nonparametric Statistics
(Sprache: Englisch)
This book gives an introduction to deconvolution problems in nonparametric statistics. It details some real-life applications as well as methodology and theory.
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Produktinformationen zu „Deconvolution Problems in Nonparametric Statistics “
This book gives an introduction to deconvolution problems in nonparametric statistics. It details some real-life applications as well as methodology and theory.
Klappentext zu „Deconvolution Problems in Nonparametric Statistics “
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 quantityh = 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.
Inhaltsverzeichnis zu „Deconvolution Problems in Nonparametric Statistics “
Density Deconvolution.- Nonparametric Regression with Errors-in-Variables.- Image and Signal Reconstruction.
Bibliographische Angaben
- Autor: Alexander Meister
- 2009, 210 Seiten, Maße: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer
- ISBN-10: 3540875565
- ISBN-13: 9783540875567
- Erscheinungsdatum: 25.03.2009
Sprache:
Englisch
Rezension zu „Deconvolution Problems in Nonparametric Statistics “
From the reviews:"This book gives an introduction to deconvolution problems in nonparametric statistics. ! The author intends to provide a comprehensive overview on results derived during the last twenty years and to give a discussion on modern and recently solved problems. ! The main target group of readers are scientists and graduate students working in mathematical statistics. ! the book is also interesting for people working in econometrics, biometrics, and other fields of applied statistics." (Hannelore Liero, Zentralblatt MATH, Vol. 1178, 2010)
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