We 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. In economic and epidemiologic studies, such segmented regression models often occur as threshold models, where it is assumed that the exposure has no influence on the response up to a possible unknown threshold. An important task of such studies is testing the existence and estimation of this threshold. Guaranteed non-asymptotic upper bounds for the significance levels of these tests are presented. We demonstrate how the proposed tests were applied toward solving an actual problem encountered with real data.