A 15min introduction to Edgeworth Expansions

This talk provides a concise introduction to Edgeworth expansions, focusing on how they refine the normal approximation by incorporating cumulants and Hermite polynomials. Starting from characteristic functions and cumulant generating functions, we build the expansion step-by-step and explain its role in improving the accuracy of confidence intervals and bootstrap methods. Both studentized and non-studentized cases are discussed, along with the related Cornish–Fisher quantile expansion. The goal is to give a practical and intuitive overview of why these expansions matter in asymptotic statistics and when they outperform classical approximations.