Estimations and Tests in Change-Point Models

This book provides a detailed exposition of the specific properties of methods of estimation and test in a wide range of models with changes. They include parametric and nonparametric models for samples, series, point processes and diffusion processes, with changes at the threshold of variables or at a time or an index of sampling.

The book contains many new results and fills a gap in statistics literature, where the asymptotic properties of the estimators and test statistics in singular models are not sufficiently developed. It is suitable for graduate students and scientific researchers working in the industry, governmental laboratories and academia.

Contents:

• Introduction
• Change-Points in the Mean
• Change-Points for Parametric Densities
• Change-Points for Parametric Regressions
• Change-Points for Point Processes
• Change-Points in Proportional Hazards Model
• Change-Points for Auto-Regressive Series
• Change-Points in Nonparametric Models
• Change-Points in Nonparametric Distributions

Readership: Graduate students and researchers in statistics, governmental laboratories and academia.
Key Features:

• The detection of changes in the distribution of observation is an important question in quality control, environmental or medical supervision
• This is a book of mathematical statistics, it covers in the same approach models for samples of independent observations and for the dependent observations of series and processes