U-statistic based on overlapping sample spacings

On the strong approximation of the non-overlapping k-spacings process with application to the moment convergence rates

“…[35] demonstrated that, for any fixed spacing size k, the Greenwood type test is optimal among type statistics-based tests (11). [35] discovered that the Greenwood type test based on overlapping k-spacings is superior to the corresponding test based on disjoint m-spacings for any fixed spacing size k. A known limitation of tests based on symmetric sum functions of spacings is their inability to detect alternatives converging to the null distribution at a rate faster than n −1/4 , for more details, refer to [44]. For applications of the spacing in statistical tests and others we may refer to [25,24], [45], [46], [8].…”