Asymptotic Results on the Greenwood Statistic and Some of its Generalizations

Abstract

SUMMARY There has been a renewed interest in the Greenwood statistic for goodness of fit and its percentage points. See Burrows (1979), Currie (1981) and Stephens (1981). This statistic, which is based on the sum of squares of the sample spacings, is known to be locally most powerful among all tests based symmetrically on the simple one-step spacings. This paper discusses some generalizations of this statistic based on higher-order or m-step spacings and shows them to be asymptotically more efficient. It is also shown that the limiting efficiency increases further if the test is based on overlapping m-step spacings as opposed to the disjoint (or non-overlapping) m-step spacings.