Del 38 i serien Cambridge Series in Statistical and Probabilistic Mathematics

Nonparametric Estimation under Shape Constraints

Estimators, Algorithms and Asymptotics

Inbunden, Engelska, 2014

1 349 kr

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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.

Produktinformation

Utgivningsdatum2014-12-11
Mått184 x 261 x 27 mm
Vikt940 g
FormatInbunden
SpråkEngelska
SerieCambridge Series in Statistical and Probabilistic Mathematics
Antal sidor428
FörlagCambridge University Press
ISBN9780521864015

Tillhör följande kategorier

Matematisk statistik inom Naturvetenskap och teknik

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.

'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