Zero bias transformation and asymptotic expansions

TL;DR

This paper introduces a recursive asymptotic expansion method using zero bias transformation to approximate expectations of functions of sums of independent random variables, including analysis of the remainder term.

Contribution

It presents a novel recursive expansion formula leveraging zero bias transformation for better approximation of sums of independent variables.

Findings

Derived a recursive asymptotic expansion formula.

Provided estimates for the remainder term.

Enhanced understanding of normal approximation accuracy.

Abstract

We apply the zero bias transformation to deduce a recursive asymptotic expansion formula for expectation of functions of sum of independent random variables in terms of normal expectations and we discuss the remainder term estimations.