Meister A. Deconvolution Problems in Nonparametric Statistics

Springer, 2009. — 208 p. — ISBN: 978-3540875567.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.Density Deconvolution
Additive Measurement Error Model
Estimation Procedures
General Consistency
Optimal Convergence Rates
Adaptive Bandwidth Selection
Unknown Error Density
Special Problems
Nonparametric Regression with Errors-in-Variables
Errors-in-Variables Problems
Kernel Methods
Asymptotic Properties
Berkson Regression
Image and Signal Reconstruction
Discrete Observation Scheme and Blind Deconvolution
White Noise Model
Circular Model and Boxcar Deconvolution
A Tools from Fourier Analysis
A.1 Fourier Transforms of L1(R)-Functions
A.2 Fourier Transforms of L2(R)-Functions
A.3 Fourier Series
A.4 Multivariate Case
B List of Symbols