Abstract
Part I has been published in the collection “Studies in the Theory of Probability Distributions. IV” (Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst., Vol. 85), Leningrad, 1979, pp. 175–187. With the aid of the methods of the branching theory of nonlinear equations, one finds a coarse asymptotics of the probabilities of large deviations for integral statistics of the form
, which are generalizations of the Cramér-von Mises-Smirnov
statistic, and also for the twosample variants of these statistics. The obtained results allow us to compute the local exact Bahadur relative asymptotic efficiency. One establishes that the latter coincides with both the Bahadur approximate and the Pitman efficiencies.
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 97, pp. 151–175, 1980.
In conclusion the author expresses his gratitude to P. Groeneboom for sending him a preprint of [11] and to H. S. Wieand for the possibility of getting acquainted with [30].
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Nikitin, Y.Y. Large deviations and asymptotic efficiency of a statistic of integral type. II. J Math Sci 24, 585–603 (1984). https://doi.org/10.1007/BF01702336
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DOI: https://doi.org/10.1007/BF01702336