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Hwang's quasi-power theorem asserts that a sequence of random variables whosemoment generating functions are approximately given by powers of some analyticfunction is asymptotically normally distributed. This theorem is generalised tohigher dimensional random variables. To obtain this result, a higherdimensional analogue of the Berry-Esseen inequality is proved, generalising atwo-dimensional version of Sadikova.

On the Higher Dimensional Quasi-Power Theorem and a Berry-Esseen Inequality