The book "Limit Theorems in Change-Point Analysis" by Miklós Csörgő and Lajos Horváth provides a comprehensive treatment of limit theorems in the context of change-point analysis. It is divided into four main chapters and an appendix, covering both parametric and nonparametric methods, linear models, and dependent observations. - **Chapter 1: The Likelihood Approach** discusses processes based on the likelihood ratio, proofs for approximations of log likelihood ratio processes, asymptotics for the maximum log likelihood ratio test, and various applications of the likelihood principle. - **Chapter 2: Nonparametric Methods** explores change in mean, location, and variance, Wilcoxon-type statistics, U-statistics, and empirical distributions. It also covers sequential ranks and more advanced nonparametric methods. - **Chapter 3: Linear Models** focuses on the maximum likelihood ratio method in linear regression, including changes in regression coefficients and variance, and consistency of tests. - **Chapter 4: Dependent Observations** examines weakly and strongly dependent sequences, procedures based on residuals, and changes in the mean of strongly dependent sequences. The appendix provides detailed proofs and approximations for various processes and distributions, making it a valuable resource for researchers and practitioners in the field of change-point analysis.The book "Limit Theorems in Change-Point Analysis" by Miklós Csörgő and Lajos Horváth provides a comprehensive treatment of limit theorems in the context of change-point analysis. It is divided into four main chapters and an appendix, covering both parametric and nonparametric methods, linear models, and dependent observations. - **Chapter 1: The Likelihood Approach** discusses processes based on the likelihood ratio, proofs for approximations of log likelihood ratio processes, asymptotics for the maximum log likelihood ratio test, and various applications of the likelihood principle. - **Chapter 2: Nonparametric Methods** explores change in mean, location, and variance, Wilcoxon-type statistics, U-statistics, and empirical distributions. It also covers sequential ranks and more advanced nonparametric methods. - **Chapter 3: Linear Models** focuses on the maximum likelihood ratio method in linear regression, including changes in regression coefficients and variance, and consistency of tests. - **Chapter 4: Dependent Observations** examines weakly and strongly dependent sequences, procedures based on residuals, and changes in the mean of strongly dependent sequences. The appendix provides detailed proofs and approximations for various processes and distributions, making it a valuable resource for researchers and practitioners in the field of change-point analysis.