Journal of Mathematical Sciences

, Volume 93, Issue 3, pp 417–420 | Cite as

Large deviations of degenerate Mises functionals

  • E. V. Ponikarov


Ya. Yu. Nikitin's method of obtaining asymptotics of large deviations is extended to a more general situation. Bibliography:14 titles.


General Situation Mise Functional 
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    M. Denker,Asymptotic Distribution Theory in Nonparametric Statistics, Vieweg, Braunschweig (1985).Google Scholar
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    G. A. M. Jeurnink and W. C. M. Kallenberg, “Limiting values of large deviation probabilities of quadratic statistics,”J. Multivariate Anal.,35, 168–185 (1990).CrossRefMathSciNetGoogle Scholar
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    Ya. Yu. Nikitin,Asymptotic Efficiency of Nonparametric Tests, Cambridge Univ. Press (1995).Google Scholar
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    Ya. Yu. Nikitin, “Large deviations and asymptotic efficiency of integral-type statistics. I,”Zap. Nauchn. Semin. LOMI,85, 175–187 (1979).MATHMathSciNetGoogle Scholar
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    Ya. Yu. Nikitin, “Large deviations and asymptotic efficiency of integral-type statistics. II,”Zap. Nauchn. Semin. LOMI,97, 151–175 (1980).MATHMathSciNetGoogle Scholar
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    I. N. Sanov, “Probabilities of large deviations of random variables,”Mat. Sb.,42 (84), 11–44 (1957).MATHMathSciNetGoogle Scholar
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    P. Groeneboom, J. Oosterhoff, and F. H. Ruymgaart, “Large deviation theorems for empirical probability measures,”Ann. Probab.,7, 553–586 (1979).MathSciNetGoogle Scholar
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    G. A. M. Jeurnink and W. C. M. Kallenberg, “Limiting exact efficiency of quadratic statistics,” Mem. No. 737, Univ. Trente (1992).Google Scholar
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© Kluwer Academic/Plenum Publishers 1999

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  • E. V. Ponikarov

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