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Nonparametric Estimation under Shape Constraints: Estimators, Algorithms and Asymptotics (Cambridge Series in Statistical and Probabilistic
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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.
- Sales Rank: #2123527 in Books
- Published on: 2014-12-15
- Original language: English
- Number of items: 1
- Dimensions: 9.96" h x 1.06" w x 6.97" l, 2.04 pounds
- Binding: Hardcover
- 428 pages
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
About the Author
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.
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