Estimations And Tests In Change-point Models (Statistics)

"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."--Publisher's website. Read more... 'This is a solid mathematical treatment of some topics in the analysis of change-point models. The book is intended for graduate students and scientific researchers using statistics in practice.' zbMATHThis 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. 'This is a solid mathematical treatment of some topics in the analysis of change-point models. The book is intended for graduate students and scientific researchers using statistics in practice.' zbMATH 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 7.1 Series of AR(p) models7.2 Convergence in the AR(1) model; 7.3 Convergence in the AR(p) model; 7.4 Change-points in AR(p) models; 7.5 Convergence in models with change-points; 7.6 Tests in models with change-points; 7.7 Change-points at a threshold of series; 8. Change-points in nonparametric models; 8.1 Nonparametric models; 8.2 Nonparametric density with a change; 8.3 Likelihood ratio test of no change; 8.4 Mixture of densities; 8.5 Nonparametric regression with a change; 8.6 Test of models without changes; 8.7 Maximum likelihood for nonparametric regressions; 8.8 Likelihood ratio test 3. Change-points for parametric densities3.1 Maximum likelihood estimation; 3.2 Likelihood ratio test; 3.3 Maximum likelihood with an unknown density; 3.4 Maximum likelihood for a chronological change; 3.5 Likelihood ratio test for a chronological change; 3.6 Nonparametric maximum likelihood; 4. Change-points for parametric regressions; 4.1 Change-points in regressions; 4.2 Convergences in linear regressions; 4.3 Test of linear regressions without change; 4.4 Change-points in parametric models; 4.5 Maximum likelihood in parametric models; 4.6 Likelihood ratio test in parametric models 5.9 Mean squares test of no change5.10 Nonparametric maximum likelihood estimators; 5.11 Likelihood ratio test of models without change; 5.12 Counting process with a multiplicative intensity; 6. Change-points in proportional hazards model; 6.1 Proportional hazards with changes; 6.2 Change-point at a covariate threshold; 6.3 Convergence of the estimators; 6.4 Maximum likelihood test of models without change; 6.5 Change-point at a time threshold; 6.6 Convergence of the estimators; 6.7 Likelihood ratio test of models without change; 7. Change-points for auto-regressive series 4.7 Chronological changes in parametric models4.8 Test of parametric models without change; 4.9 Maximum likelihood for chronological changes; 4.10 Likelihood ratio test; 5. Change-points for point processes; 5.1 Change in the intensity of a Poisson process; 5.2 Likelihood ratio test for a Poisson process; 5.3 Parametric models for Poisson processes; 5.4 Likelihood ratio test for parametric processes; 5.5 Counting process with right censoring; 5.6 Change-point in a hazard function; 5.7 Parametric estimators under right-censoring; 5.8 Estimation by minimum of variance Intro; Contents; Preface; 1. Introduction; 1.1 Detection of changes in the distribution of a sample; 1.2 Change-points in regression models; 1.3 Models for processes; 1.4 Empirical processes on small intervals; 1.5 Content of the book; 2. Change-points in the mean; 2.1 Empirical estimators; 2.2 Test for a change of mean; 2.3 Maximum likelihood estimation; 2.4 Likelihood ratio test; 2.5 Maximum likelihood with an unknown density; 2.6 Chronological change in the mean; 2.7 Maximum likelihood for a chronological change; 2.8 Nonparametric maximum likelihood