Non-asymptotic results for Cornish--Fisher expansions

TL;DR

This paper derives computable error bounds for generalized Cornish-Fisher expansions of quantiles, contingent on known bounds for Edgeworth-Chebyshev expansions, and illustrates these results with examples.

Contribution

It provides a method to obtain explicit error bounds for Cornish-Fisher expansions based on existing bounds for Edgeworth-Chebyshev expansions, enhancing their practical applicability.

Findings

Derived explicit error bounds for Cornish-Fisher expansions

Connected error bounds to Edgeworth-Chebyshev expansions

Validated results through illustrative examples

Abstract

We get the computable error bounds for generalized Cornish-Fisher expansions for quantiles of statistics provided that the computable error bounds for Edgeworth-Chebyshev type expansions for distributions of these statistics are known. The results are illustrated by examples.