Sequential detection of switches in models with changing structures. Issue 3 (2nd April 2016)

• Record Type: Journal Article
• Authors: Brodsky, Boris; Darkhovsky, Boris
• Is Part Of: Stochastics. Volume 88:Issue 3(2016)
• Page Start: 460
• Page End: 479
• Publication Date: 2016-04-02
• Subjects: Change-point -- stochastic switches -- type 1 and type 2 errors -- performance measure -- Monte Carlo tests; 62L10; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2015.1086349
• Languages: English
• ISSNs: 1744-2508

Abstract

Abstract : Models with a changing structure, and in particular with switches in a model's parameters, are often used in applications. In this paper we consider sequential detection of such fully stochastic switches of parameters and propose the nonparametric and asymptotically optimal method for detection of switches. We prove that type 1 and type 2 errors of detection converge to zero exponentially for dependent sequences of observations satisfying Cramer's and -mixing conditions as the number of observations increases to infinity. The asymptotic optimality result is proved for the main performance criterion of detection (convergence of estimates to the true values of parameters). Results of experimental testing of the proposed method and its comparison with other detection techniques are given.