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OverviewThis 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. Full Product DetailsAuthor: Piet Groeneboom (Technische Universiteit Delft, The Netherlands) , Geurt Jongbloed (Technische Universiteit Delft, The Netherlands) , Jon A. WellnerPublisher: Cambridge University Press Imprint: Cambridge University Press Volume: 38 Dimensions: Width: 18.40cm , Height: 2.70cm , Length: 26.10cm Weight: 0.940kg ISBN: 9780521864015ISBN 10: 0521864011 Pages: 428 Publication Date: 11 December 2014 Audience: College/higher education , Postgraduate, Research & Scholarly Format: Hardback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of Contents1. 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.Reviews'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 Author InformationPiet 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. Tab Content 6Author Website:Countries AvailableAll regions |
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