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

TL;DR

This paper extends Hwang's quasi-power theorem to higher dimensions and introduces a multidimensional Berry-Esseen inequality, broadening the scope of asymptotic normality results for complex random variable sequences.

Contribution

The paper generalizes the quasi-power theorem and the Berry-Esseen inequality to higher dimensions, providing new tools for analyzing the distribution of multivariate random variables.

Findings

Established a higher dimensional analogue of the Berry-Esseen inequality.

Extended Hwang's quasi-power theorem to multivariate cases.

Provided theoretical foundations for asymptotic normality in higher dimensions.

Abstract

Hwang's quasi-power theorem asserts that a sequence of random variables whose moment generating functions are approximately given by powers of some analytic function is asymptotically normally distributed. This theorem is generalised to higher dimensional random variables. To obtain this result, a higher dimensional analogue of the Berry-Esseen inequality is proved, generalising a two-dimensional version of Sadikova.