Significance levels of linear rank tests using Edgeworth expansions

We study one aspect of applying Edgeworth expansions to linear rank statistics. Since the use of such expansions is often recommended already for moderate sample sizes we investigate for this case the gain of accuracy for the level of significance of some linear rank tests when their critical values are derived from an Edgeworth expansion instead of from a normal approximation. We verify Does' conditions (1983) for the validity of the expansions for four rank statistics of general interest and show by a numerical study that an Edge‐worth expansion does not outperform the normal approximation in all situations. A considerable improvement shows up however for the Klotz test at the 5% level.