On a distribution-free test of fit for continuous distribution functions

This paper studies a test for goodness-of-fit based on what sill here be called the normalized log spacing statistic (NLSS statistic), The NLSS statistic is related to the Moran statistic (Moran, 1951; Cheng & Stephens, 1989). The NLSS test of fit is here shown to be comparable to the Kolmogorov-Smirnov test with respect to universal features such as being distribution-free and consistent against all continuous alternatives. A well-known result of Chibisov (1961) asserts that the Pitman asymptotic relative efficiency of the NLSS test to the Kolmogorov-Smirnov test can be zero for a sequence of ''smooth'' alternatives. It is shown that the Kolmogorov-Smirnov type tests to the NLSS test have zero Pitman asymptotic relative efficiency for some non-smooth sequences of alternatives.