This paper is concerned with the exact Bahadur efficiencies of spacings statistics. For a general class of statistics based on a fixed number of spacings, the explicit forms of the exact slopes are derived, and it is shown that the sum of the logarithms of spacings is optimal in this class. Some results are extended to the case where the number of spacings increase with the sample size to infinity. © 1989 The Institute of Statistical Mathematics.

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.