On Greenwood goodness-of-fit test

sThe Greenwood test is based on the sum of squares of disjoint spacings. For the goodness-of-fit problem within the class of symmetric tests, the Greenwood test is known to be optimal in terms of the Pitman asymptotic efficiency (AE), whereas it is much inferior to the log-spacings test in terms of the Bahadur AE. In this paper we extend these properties of Greenwood test showing that it remains optimal in terms of the weak intermediate and intermediate AE, but it is much inferior to those tests satisfying the Cramer condition in terms of the strong intermediate AE.