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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.
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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)
"Research workers in mathematical statistics. ... The target readership is described as 'scientists and graduate students working in the field of mathematical statistics' ... . Throughout, there are lots of proofs and derivations, particularly involving estimation consistency and convergence rates. ... This looks to me like an excellent book for the specialist - a thorough, detailed, rigorous treatment of a particular field." (Martin Crowder, International Statistical Review, Vol. 78 (1), 2010)
"Deconvolution problems occur in many topics of nonparametric statistics with ample applications in other scientific fields. This book focuses on methodology and theory rather than computational aspects and programming. ... In summary, this book is quite theoretical. It is written in a tutorial style and it makes a good self-teaching monograph for the methodology and theory development of deconvolution problems." (Su-Yun Chen Huang, Mathematical Reviews, Issue 2012 h)
"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)
"Research workers in mathematical statistics. ... The target readership is described as 'scientists and graduate students working in the field of mathematical statistics' ... . Throughout, there are lots of proofs and derivations, particularly involving estimation consistency and convergence rates. ... This looks to me like an excellent book for the specialist - a thorough, detailed, rigorous treatment of a particular field." (Martin Crowder, International Statistical Review, Vol. 78 (1), 2010)
"Deconvolution problems occur in many topics of nonparametric statistics with ample applications in other scientific fields. This book focuses on methodology and theory rather than computational aspects and programming. ... In summary, this book is quite theoretical. It is written in a tutorial style and it makes a good self-teaching monograph for the methodology and theory development of deconvolution problems." (Su-Yun Chen Huang, Mathematical Reviews, Issue 2012 h)