Nonparametric Estimation under Shape Constraints: Estimators, Algorithms and Asy

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Nonparametric Estimation under Shape Constraints by Piet Groeneboom, Geurt Jongbloed

This book treats the latest developments in the theory of order-restricted inference, with special attention to nonparametric methods and algorithmic aspects. 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.

FORMAT
Hardcover LANGUAGE
English CONDITION
Brand New Publisher 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.

Table of Contents

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.

Review

'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

Promotional

This book introduces basic concepts of shape constrained inference and guides the reader to current developments in the subject.

Review Quote

'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

Promotional \"Headline\"

This book introduces basic concepts of shape constrained inference and guides the reader to current developments in the subject.

Description for Bookstore

This book treats the latest developments in the theory of order-restricted inference, with special attention to nonparametric methods and algorithmic aspects. 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.

Description for Library

This book treats the latest developments in the theory of order-restricted inference, with special attention to nonparametric methods and algorithmic aspects. 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.

Details ISBN0521864011 Author Geurt Jongbloed Publisher Cambridge University Press ISBN-10 0521864011 ISBN-13 9780521864015 Format Hardcover Imprint Cambridge University Press Subtitle Estimators, Algorithms and Asymptotics Place of Publication Cambridge Country of Publication United Kingdom DEWEY 519.544 Pages 428 Media Book Year 2014 Publication Date 2014-12-11 Short Title NONPARAMETRIC ESTIMATION UNDER Language English Series Number 38 Affiliation Technische Universiteit Delft, The Netherlands Illustrations Worked examples or Exercises; 20 Tables, unspecified; 90 Line drawings, unspecified UK Release Date 2014-12-11 AU Release Date 2014-12-11 NZ Release Date 2014-12-11 Series Cambridge Series in Statistical and Probabilistic Mathematics Alternative 9781139020893 Audience Postgraduate, Research & Scholarly Country of Origin US Product Class Description Mathematics
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