Rearranging Edgeworth-Cornish-Fisher Expansions

TL;DR

This paper introduces a rearrangement technique to improve the monotonicity and accuracy of Edgeworth and Cornish-Fisher expansions for distribution and quantile functions, enhancing their practical utility.

Contribution

It proposes a regularization method called increasing rearrangement to monotonize and significantly improve the approximations of distribution and quantile functions.

Findings

Rearranged expansions satisfy monotonicity.

Improved approximation accuracy observed.

Method applicable to various related expansions.

Abstract

This paper applies a regularization procedure called increasing rearrangement to monotonize Edgeworth and Cornish-Fisher expansions and any other related approximations of distribution and quantile functions of sample statistics. Besides satisfying the logical monotonicity, required of distribution and quantile functions, the procedure often delivers strikingly better approximations to the distribution and quantile functions of the sample mean than the original Edgeworth-Cornish-Fisher expansions.