
Nonparametric Estimation under Shape Constraints
Estimators, Algorithms and Asymptotics
Cambridge University Press
Published on 11. December 2014
Book
Hardback
428 pages
978-0-521-86401-5 (ISBN)
Description
This book treats the latest developments in the theory of order-restricted inference, with special attention to nonparametric methods and algorithmic aspects. Among the topics treated are current status and interval censoring models, competing risk models, and deconvolution. Methods of order restricted inference are used in computing maximum likelihood estimators and developing distribution theory for inverse problems of this type. The authors have been active in developing these tools and present the state of the art and the open problems in the field. The earlier chapters provide an introduction to the subject, while the later chapters are written with graduate students and researchers in mathematical statistics in mind. Each chapter ends with a set of exercises of varying difficulty. The theory is illustrated with the analysis of real-life data, which are mostly medical in nature.
Reviews / Votes
'Shape constraints arise naturally in many statistical applications and are becoming increasingly popular as a means of combining the best of the parametric and nonparametric worlds. This book, written by two experts in the field, gives a detailed treatment of many of their attractive features. I have no doubt it will be a valuable resource for researchers, students, and others interested in learning about this fascinating area.' Richard Samworth, University of Cambridge 'I recommend this impressive book very enthusiastically to both young and senior researchers interested in shape-restricted nonparametric estimation. Closing an important gap in the literature, it contains not only classical material on nonparametric estimation of monotone functions in a series of application fields but also an introduction to advanced themes that are the topic of active ongoing research - in particular, estimation of convex functions, interval censoring, higher dimensional models, and other complex models in order-restricted inference. Interesting and enjoyable, the book clearly motivates models and methods by illustrative data examples and intuitive heuristic explanations of the necessary asymptotic mathematical theory, accompanied by clear and detailed proofs of the theory.' Enno Mammen, Institute of Applied Mathematics, Heidelberg University 'A comprehensive study of the state of the art in nonparametric shape-restricted inference by two experts in the field. A clear-cut cogent presentation style, along with a careful exposition of the mathematics as well as the algorithmic aspects of the optimization problems involved, makes this a very well-rounded text that should prove an asset to both mathematically trained scientists seeking a rigorous exposure to the field and statistical researchers interested in the 'current status' of affairs in shape-restricted inference.' Moulinath Banerjee, University of Michigan, Ann Arbor 'The book provides an up-to-date comprehensive review of both classical and new methods for shape constrained estimators. It does so in a clear and well-explained manner, including many real-world examples to motivate the methodology and theory. As such it contains a nice mix of theory and applications, and so should be of interest to both students and researchers. ... I thoroughly enjoyed reading this book: it gives a detailed treatment of most relevant features of shape constrained estimation, and does so in a manner that makes it immensely readable, whether you are a novice or an expert in the area.' Dennis Kristensen, MathSciNet Mathematical Reviews (www.ams.org/mr-database)More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
College/higher education
Illustrations
Worked examples or Exercises; 20 Tables, unspecified; 90 Line drawings, unspecified
Dimensions
Height: 260 mm
Width: 183 mm
Thickness: 28 mm
Weight
999 gr
ISBN-13
978-0-521-86401-5 (9780521864015)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions

Piet Groeneboom
Nonparametric Estimation under Shape Constraints
Estimators, Algorithms and Asymptotics
E-Book
12/2014
Cambridge University Press
€63.99
Available for download

Piet Groeneboom | Geurt Jongbloed
Nonparametric Estimation under Shape Constraints
Estimators, Algorithms and Asymptotics
E-Book
11/2014
1st Edition
Cambridge University Press
€76.99
Available for download
Persons
Piet Groeneboom is Professor Emeritus of Statistics at Delft University of Technology, The Netherlands. Geurt Jongbloed is Professor of Statistics at Delft University of Technology, The Netherlands.
Author
Technische Universiteit Delft, The Netherlands
Technische Universiteit Delft, The Netherlands
Content
1. Introduction; 2. Basic estimation problems with monotonicity constraints; 3. Asymptotic theory for the basic monotone problems; 4. Other univariate problems involving monotonicity constraints; 5. Higher dimensional problems; 6. Lower bounds on estimation rates; 7. Algorithms and computation; 8. Shape and smoothness; 9. Testing and confidence intervals; 10. Asymptotic theory of smooth functionals; 11. Pointwise asymptotic distribution theory for univariate problems; 12. Pointwise asymptotic distribution theory for multivariate problems; 13. Asymptotic distribution of global deviations.