On the Convexity of a Rate Function - P.T, Choon (Malaysian Journal of Science, 2006)
Consider a sequence of independent, identically distributed random variables from a common distribution . Suppose that there are rare events associated with , for example events involving the sample moments. Then the dominant rate at which the probability of the intersection of the events converges to zero can be expressed as the relative entropy of a certain distribution and . Considering the intersection of the events as a function of in a -dimensional Euclidean space, we shall show that the dominant rate of convergence is convex in . This result is the consequence of the convex property of a certain function associated with the dominant rate of convergence which shall be shown