We study approximations to the distribution of the largest Walsh-Fourier coefficient obtained by transforming i.i.d. observations from a non-normal parent distribution. The study is inspired by the use of half-normal plots in screening studies and in the analysis of molecular sequence data. In the latter context, we indicate why continuity corrections are needed.
"Asymptotics for the maximum of half-normal plots." Ann. Statist. 24 (5) 2250 - 2265, October 1996. https://doi.org/10.1214/aos/1069362320