Minimum Chernoff entropy and exponential bounds for locating changes

Large deviation theory makes extensive use of Chernoff exponential bounds to establish exert rates of convergence for certain probabilities. In this article, stronger exponential bounds from martingale theory are utilized to give results on the errors of the maximum-likelihood estimate of the location of a change between two probability measures in terms of the minimum Chernoff entropy (MCE). For example, the probability of estimating the change point exactly is bigger than one minus twice the MCE. These results support the use of the MCE as an appropriate distance measure between probability measures for applications such as the automatic classification of digital modulation signal constellations.