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- W2004697780 abstract "1. Introduction. In 1960, Bahadur [3] proposed two measures of the asymptotic performance of tests: one approximate measure, based on the limiting distribution of the test statistic; and one exact, based on the limiting form of the probability of a large deviation of the statistic from its asymptotic mean. Although knowledge of the exact measure is more desirable, it is often difficult to compute, whereas the approximate measure is usually trivially available. It is to be hoped that the approximate measure will nearly always be a good approximation to the exact measure, and there is considerable evidence in support of this conjecture, but counterexamples do exist (see e.g. [1], p. 20). This paper explores the question for the Kolmogorov-Smirnov (K-S) and Kuiper statistics-two closely related measures of goodness-of-fit based on deviations of the sample distribution functions from the null case-in one- and two-sample situations. In the case of the weighted one-sample K-S statistic and the two-sample Kuiper statistic, it is possible to obtain exact measures although the corresponding approximate measures are not available. The relative efficiency (in a sense defined in Section 2) of the weighted one-sample K-S statistic to the unweighted K-S statistic is computed in a number of cases, and the relative efficiency of the Kuiper statistic to the unweighted K-S statistic is also examined, from which it appears that the Kuiper statistic is always at least as good (and often much better) than the K-S statistic. In the cause of brevity, a great deal of the theory and all the computational detail (generally very tedious) has been omitted. Much of it is available in [1]. However, a short resum6 of the theory of the Bahadur measures of performance and their properties is given in Section 2 for the sake of completeness, although the details here are also omitted." @default.
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- W2004697780 date "1967-10-01" @default.
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- W2004697780 title "Exact Bahadur Efficiencies for the Kolmogorov-Smirnov and Kuiper One- and Two-Sample Statistics" @default.
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- W2004697780 doi "https://doi.org/10.1214/aoms/1177698702" @default.
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