On a lower bound for Fisher information by moment-generating function

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Fisher information plays crucial roles in statistics, while the moment-generating function provides a fundamental specification of probability density functions appeared in a variety of fields. In terms of the moment-generating function, we present a general form of the lower bound on Fisher information associated with parametric statistical models. The bound is derived from Cauchy-Schwarz inequality. We discuss the consequences of employing different inequalities and compare our results with the previously derived moments-based lower bound.