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.
Contains many exercises (190)
Utilizes recent research in the field
Covers both mathematical and algorithmic aspects
Author(s): Piet Groeneboom, Geurt Jongbloed
Series: Cambridge Series in Statistical and Probabilistic Mathematics
Publisher: Cambridge University Press
Year: 2014
Language: English
Pages: C, xii, 428
Tags: Математика;Теория вероятностей и математическая статистика;Математическая статистика;
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.
