We construct new tests of exponentiality based on Rossberg’s characterization of the exponential law. We compute limiting distributions of new tests, local Bahadur efficiency for common alternatives, and describe conditions of their local asymptotic optimality. Bibliography: 13 titles.
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References
V. S. Korolyuk and Yu. V. Borovskikh, Theory of U-statistics [in Russian], Kiev (1989).
V. V. Litvinova, "Asymptotic properties of symmetry and goodness-of-fit tests based on characterizations," PhD Thesis, St. Petersburg State Univ. (2004).
Ya. Yu. Nikitin, Asymptotic Efficiency of Nonparametric Statistical Tests [in Russian], Moscow (1995).
Ya. Yu. Nikitin and E. V. Ponikarov, "Rough asymptotic of probabilities of Chern of type large deviations for von Mises functionals and U-statistics," Tr. St. Peterb. Math. Soc., 7, 124–167 (1999).
A. V. Chirina, "Asymptotic efficiency of exponentiality tests that are free of scale parameter," PhD Thesis, St. Petersburg State Univ. (2005).
R. R. Bahadur, "Rates of convergence of estimates and test statistics," Ann. Math. Stat., 38, 303–324 (1967).
P. L. Janssen, Generalized Empirical Distribution Functions with Statistical Applications, Limburgs Univ. Centrum, Diepenbeek (1988).
Ya. Yu. Nikitin, "Large deviations of U-empirical Kolmogorov–Smirnov tests, and their efficiency," J. Nonparam. Statistics (2010).
Ya. Yu. Nikitin, "U-statistical Kolmogorov–Smirnov tests: large deviations and asymptotic efficiiency," in: J. C. Fernandez-Pardo and J. de Una-Alvarez (eds), Proc. ISNI2008 Vigo (2008), pp. 138–142.
Ya. Yu. Nikitin and A. V. Tchirina, "Bahadur efficiency and local optimality of a test for the exponential distribution based on the Gini statistic," J. Ital. Statist. Soc., 5, 163–175 (1996).
H.-J. Rossberg, "Characterization of the exponential and the Pareto distributions by means of some properties of the distributions which differences and quotients of order statistics are subjected to," Math. Operat. Statist., 3, 207–216 (1992).
M. Riedel and H.-J. Rossberg, "Characterization of the exponential distribution function by properties of the difference X k+s:n − X k:n of order statistics," Metrika, 41, 1–19 (1994).
B. W. Silverman,"Convergence of a class of empirical distribution functions of dependent random variables," Ann. Probab., 11, 745–751 (1983).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 368, 2009, pp. 95–109.
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Volkova, K.Y. On asymptotic efficiency of exponentiality tests based on Rossberg’s characterization. J Math Sci 167, 486–494 (2010). https://doi.org/10.1007/s10958-010-9934-9
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DOI: https://doi.org/10.1007/s10958-010-9934-9