On the asymptotic distributions of high-order spacings statistics

Goodness-of-fit tests for the uniform distribution based on sums of smooth functions of m-spacings are studied. A limiting sum-of-weighted-chi-squareds approximation is shown to be accurate uniformly in m for the special cases of analogues of Greenwoo?s statistic and Moran's statistic. Asymptotic critical points are provided; theory and Monte Carlo studies show they are accurate for all m provided n is moderately large.