UC Santa Barbara

Tests based on higher-order or m-step spacings have been considered in the literature for the goodness of fit problem. This paper studies the asymptotic distribution theory for such tests based on non-overlapping m-step spacings when m, the length of the step, also increases with the sample size n, to inifinity. By utilizing the asymptotic distributions under a sequence of close alternatives and studying their relative efficiencies, we try to answer a central question about the choice of m in relation to n. Efficiency comparisons are made with tests based on overlapping m-step spacings, as well as corresponding chi-square tests. © 1989, Physica-Verlag Ges.m.b.H. All rights reserved.