Deconvolution Problems in Nonparametric Statistics
Language: English
Published by Springer, 2009
- Softcover
- New
Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH
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Add to basketItem description from seller
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 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.…
Seller Inventory # 9783540875567
- Title
- Deconvolution Problems in Nonparametric Statistics
- Author
- Alexander Meister
- Publisher
- Springer
- Publication year
- 2009
- Condition
- Neu
- Binding
- Taschenbuch
- Language
- English
- ISBN 10
- 3540875565
- ISBN 13
- 9783540875567
- Item weight
- 335 grams
- Dimensions
- 235x155x12 mm
- Series
- Book 41 of 72: Lecture Notes in Statistics
This book gives an introduction to deconvolution problems in nonparametric statistics. It details some real-life applications as well as methodology and theory.
"Synopsis" may belong to another edition of this title.
From the Back Cover
This book gives an introduction to deconvolution problems in nonparametric statistics, e.g. density estimation based on contaminated data, errors-in-variables regression, and image reconstruction. Some real-life applications are discussed while we mainly focus on methodology (description of the estimation procedures) and theory (minimax convergence rates with rigorous proofs and adaptive smoothing parameter selection). In general, we have tried to present the proofs in such manner that only a low level of previous knowledge is needed. An appendix chapter on further results of Fourier analysis is also provided.
"About the title" may belong to another edition of this title.
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