Asymptotic distribution of independent random vectors given their sum

TL;DR

This paper develops a Gibbs-type conditional principle for independent, non-identically distributed vectors using Edgeworth expansions to analyze the asymptotic distribution of their sums.

Contribution

It introduces a new conditional principle for non-i.i.d. vectors based on Edgeworth expansions, extending existing theories.

Findings

Established a Gibbs-type conditional distribution for sums of independent vectors.

Derived asymptotic distributions using Edgeworth expansions.

Extended classical results to non-i.i.d. settings.

Abstract

In this paper we present a conditional principle of Gibbs type for independent nonidentically distributed random vectors. We obtain this result by performing Edgeworth expansions for densities of sums of independent random vectors.