2011/10/26 by Boris Brodsky, Brodsky, Boris, B. S. Darkhovsky +2
Mathematics · #Advanced Statistical Methods and Models #Algorithm #Applied mathematics #Artificial intelligence #Change detection #Computer science #Convergence (economics) #Estimation #FOS: Mathematics #Mathematics #Multivariate statistics #Point (geometry) #Point estimation #Statistical Methods and Inference #Statistical and numerical algorithms #Statistics #Statistics Theory (math.ST) #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.1110.5731
published in arXiv (Cornell University) (Cornell University)
arxiv created 2011/10/26 · openalex publication_date 2011/10/26 · arxiv updated 2011/10/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this paper the problem of retrospective change-point detection and estimation in multivariate linear models is considered. The lower bounds for the error of change-point estimation are proved in different cases (one change-point: deterministic and stochastic predictors, multiple change-points). A new method for retrospective change-point detection and estimation is proposed and its main performance characteristics (type 1 and type 2 errors, the error of estimation) are studied for dependent observations in situations of deterministic and stochastic predictors and unknown change-points. We prove that this method is asymptotically optimal by the order of convergence of change-point estimates to their true values as the sample size tends to infinity. Results of a simulation study of the main performance characteristics of proposed method in comparison with other well known methods of retrospective change-point detection and estimation are presented.