Nonparametric Estimation under Shape Constraints

Estimators, Algorithms and Asymptotics

AvPiet Groeneboom,Geurt Jongbloed

Inbunden, Engelska, 2014

Del 38 i serien Cambridge Series in Statistical and Probabilistic Mathematics

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2014-12-11
Mått:184 x 261 x 27 mm
Vikt:940 g
Format:Inbunden
Språk:Engelska
Serie:Cambridge Series in Statistical and Probabilistic Mathematics
Antal sidor:428
Förlag:Cambridge University Press
ISBN:9780521864015

Utforska kategorier

Matematisk statistik inom Naturvetenskap och teknik

Mer om författaren

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.

Recensioner i media

'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

Innehållsförteckning

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.