Error Exponents in Hypothesis Testing and Chernoff Information - C.P, Tan, (Malaysian Journal of Science, 2007)
We consider a simple hypothesis testing problem on the parameters of a probability distribution belonging to the exponential class. It is well-known that the Chernoff information is the best asymptotic achievable exponent in the Bayesian probability of error when we use a likelihood ratio test with an exponential threshold function of the sample size. We shall derive the general forms of the error exponent and the Chernoff information for the exponential class. In tests using the maximum-a-posteriori probability decision rule, the Chernoff information provides a lower bound on the error exponent. The Chernoff informations of some common distributions will be demonstrated.