Communications in Statistics: Theory and Methods vol:30 issue:7 pages:1435-1470
Following (1), (2) and (3), who proposed a test of uniformity based on m-th order disjoint sample spacings, we propose its analog based on m-th order overlapping sample spacings. Three interesting and intuitively appealing motivations, in favor of the proposed test procedure, are given. Asymptotic, normality of the proposed test statistic is derived under the null hypothesis and under a large class of fixed alternatives. The proposed test procedure is shown to be consistent against a large class of alternatives. For a sequence of local alternatives, which, converges to the null hypothesis at the rate of n(-1/4), the proposed test procedure is compared with three existing test procedures (i.e. the Greenwood-type test procedure proposed in (4), which is known to be locally most powerful among all test procedures based symmetrically on spacings, a procedure due to (5) and a procedure due to (3)), in terms of the Pitman asymptotic relative efficiency. It is observed that the proposed test procedure has larger efficacies than test procedures proposed by (5) and (3), and has efficacies comparable to the Greenwood-type test procedure. Using Monte Carlo simulations, we simulate finite sample critical points and power results against seven alternatives. We observe that, compared with other tests of uniformity, our test possesses good power properties for many alternatives.