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: IntroductionChange-Points in the MeanChange-Points for Parametric DensitiesChange-Points for Parametric RegressionsChange-Points for Point ProcessesChange-Points in Proportional Hazards ModelChange-Points for Auto-Regressive SeriesChange-Points in Nonparametric ModelsChange-Points in Nonparametric Distributions
Readership: Graduate students and researchers in statistics, governmental laboratories and academia.
Change-Points;Test Statistics;Estimation;Detection;Mean;Parametric and Nonparametric Models;Density;Regression;Point Process;Diffusion;Series;Maximum Likelihood;Least Squares Estimator0Key Features:The detection of changes in the distribution of observation is an important question in quality control, environmental or medical supervisionThis 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