Guaranteed testing for epidemic changes of a linear regression model

The objective of this paper is to propose and examine a class of generalized maximum likelihood asymptotic power one tests for detection of various types of changes in a linear regression model. The proposed retrospective tests are based on martingales structures Shiryayev-Roberts statistics. This approach is widely known in a sequential analysis of change point problems as an optimal method of detecting a change in distribution. Guaranteed non-asymptotic upper bounds for the significance levels of the considered tests are presented. Simulated data sets are used to demonstrate that the proposed tests can give good results in practice.