Abstract
Limit distributions for certain statistics of Smirnov — Kolmogorov type are obtained which consider the weak convergence of the corresponding empirical process. Approximate and precise asymptotic efficiencies of these statistics are computed. It is shown that they are worse in a certain sense than the classical Kolmogorov — Smirnov statistics.
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 55, pp. 185–194, 1976.
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Nikitin, Y.Y. Limit distributions and comparative asymptotic efficiency of the Smirnov — Kolmogorov statistics with a random index. J Math Sci 16, 1042–1049 (1981). https://doi.org/10.1007/BF01676147
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DOI: https://doi.org/10.1007/BF01676147