Nonparametric Estimation under Shape Constraints
Estimators, Algorithms and Asymptotics

This book introduces basic concepts of shape constrained inference and guides the reader to current developments in the subject.

Piet Groeneboom (Author), Geurt Jongbloed (Author)

9780521864015, Cambridge University Press

Hardback, published 11 December 2014

428 pages, 90 b/w illus. 20 tables 190 exercises
26.1 x 18.4 x 2.7 cm, 0.94 kg

'The book provides an up-to-date comprehensive review of both classical and new methods for shape constrained estimators. It does so in a clear and well-explained manner, including many real-world examples to motivate the methodology and theory. As such it contains a nice mix of theory and applications, and so should be of interest to both students and researchers. … I thoroughly enjoyed reading this book: it gives a detailed treatment of most relevant features of shape constrained estimation, and does so in a manner that makes it immensely readable, whether you are a novice or an expert in the area.' Dennis Kristensen, MathSciNet Mathematical Reviews (www.ams.org/mr-database)

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.

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.

Subject Areas: Meteorology & climatology [RBP], Probability & statistics [PBT], Economic statistics [KCHS], Economics [KC]