Deconvolution Problems Nonparametric Statistics by Meister Alexander (9 results)
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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 to…pics 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.
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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 d…ecades, 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. 216 pp. Englisch.
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Published by Springer Berlin Heidelberg, 2009
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Gives a general unifying approach to statistical deconvolution topics with easy to understand proofs and applicationsDeconvolution problems occur in many ?elds of nonparametric statistics, for example, density estimat…ion based on contaminated data, nonp.
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Published by Springer, Springer Vieweg Mär 2009, 2009
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Taschenbuch. Condition: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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 decad…es, 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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 216 pp. Englisch.
