Nonparametric estimation under shape constraints : estimators, algorithms, and asymptotics
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Bibliographic Information
Nonparametric estimation under shape constraints : estimators, algorithms, and asymptotics
（Cambridge series on statistical and probabilistic mathematics）
Cambridge University Press, 2014
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Includes bibliographical references (p. 401-408) and index
Description and Table of Contents
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.
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