A comparison of unconditional and conditional solutions to the maximum likelihood estimation of a change-point.
We compare the performance of unconditional and conditional solutions to the problem of estimating an unknown change-point by the method of maximum likelihood estimation. We begin by presenting some asymptotic results for the first two moments of the unconditional solution. Then, considering the cases of normal and exponential distributions, we evaluate through simulations the accuracy of large sample distribution theory results for the above two solutions through bias, mean square error, and graphical displays. In both normal and exponential cases, the unconditional solution shows better performance whenever the amount of change is small and when the true parameters are unknown. The differences are particular sharp when the true change-point is towards the tail of the data. When the amount of change is large, both methods perform at similar levels of accuracy. Finally, we illustrate the two solutions through data on British coal mine explosions.
scientific article; zbMATH DE number 1521706