A NEW TEST OF UNIFORMITY BASED ON OVERLAPPING SAMPLE SPACINGS

Following 1-2 Gebert, J. B. and Kale, B. K. 1969. Goodness of Fit Tests Based on Discriminatory Information. Statist. Hefte., 10: 192–200. Jammalamadaka, S. R. and Tiwari, R. C. 1985. Asymptotic Comparison of Three Tests for Goodness of Fit. J. Statist. Plann. Inf., 12: 295–304. and [3] Jammalamadaka, S. R. and Tiwari, R. C. 1987. “Efficiencies of Some Disjoint Spacings Tests Relative to a Chi-square Test”. In New Perspectives in Theoretical and Applied Statistics Edited by: Puri and et. al. 311–317. New York: Wiley. [Google Scholar], who proposed a test of uniformity based on m-th order disjoint sample spacings, we propose its analog based on m-th order overlapping sample spacings. Three interesting and intuitively appealing motivations, in favor of the proposed test procedure, are given. Asymptotic normality of the proposed test statistic is derived under the null hypothesis and under a large class of fixed alternatives. The proposed test procedure is shown to be consistent against a large class of alternatives. For a sequence of local alternatives, which converges to the null hypothesis at the rate of n −1/4 the proposed test procedure is compared with three existing test procedures (i.e. the Greenwood-type test procedure proposed in [4] Greenwood, M. 1946. The Statistical Study of Infectious Diseases. J. Roy. Statist. Soc. A, 109: 85–110. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar], which is known to be locally most powerful among all test procedures based symmetrically on spacings, a procedure due to [5] Cressie, N. 1976. On the Logarithms of High-Order Spacings. Biometrika, 63: 343–355. [Crossref], [Web of Science ®] , [Google Scholar] and a procedure due to [3] Jammalamadaka, S. R. and Tiwari, R. C. 1987. “Efficiencies of Some Disjoint Spacings Tests Relative to a Chi-square Test”. In New Perspectives in Theoretical and Applied Statistics Edited by: Puri and et. al. 311–317. New York: Wiley. [Google Scholar]), in terms of the Pitman asymptotic relative efficiency. It is observed that the proposed test procedure has larger efficacies than test procedures proposed by [5] Cressie, N. 1976. On the Logarithms of High-Order Spacings. Biometrika, 63: 343–355. [Crossref], [Web of Science ®] , [Google Scholar] and [3] Jammalamadaka, S. R. and Tiwari, R. C. 1987. “Efficiencies of Some Disjoint Spacings Tests Relative to a Chi-square Test”. In New Perspectives in Theoretical and Applied Statistics Edited by: Puri and et. al. 311–317. New York: Wiley. [Google Scholar], and has efficacies comparable to the Greenwood-type test procedure. Using Monte Carlo simulations, we simulate finite sample critical points and power results against seven alternatives. We observe that, compared with other tests of uniformity, our test possesses good power properties for many alternatives.

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