The likelihood ratio method for testing changes in the parameters of double exponential observations

Several papers have been published on the change point problem in location models. Majority of them uses least squares type methods. The least absolute deviation estimator of change point was studied in Bai (Econom. Theory 11 (1995) 403). Horv?th (Ann. Statist. 21 (1993) 671) derived the least squares statistic for location and scale models. In the present paper, we focus on location and scale models and we use the least absolutes deviation methods. We construct a test statistic and a change point estimator and establish their limit behaviour.