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Mathematics of the USSR-Izvestiya, 1983, Volume 20, Issue 3, Pages 535–576
DOI: https://doi.org/10.1070/IM1983v020n03ABEH001620 (Mi im1627) 		 
On asymptotic admissibility of goodness-of-fit tests

A. N. Tyulyagin
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DOI: https://doi.org/10.1070/IM1983v020n03ABEH001620
Abstract: Asymptotic properties of goodness-of-fit tests for testing simple and composite parametric hypotheses with continual alternatives are studied. The author investigates conditions under which goodness-of-fit tests are asymptotically admissible. He considers the question of completeness of the class of asymptotically admissible goodness-of-fit tests. To solve these problems he studies the properties of admissible tests for the limit problem of testing the hypothesis about the mean of a Gaussian random element in Hilbert space. As an application of the results he proves asymptotic admissibility and nonadmissibility of various goodness-of-fit tests used in practice.
Bibliography: 31 titles.
Received: 20.07.1981
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1982, Volume 46, Issue 3, Pages 569–616
Bibliographic databases:
UDC: 519.234.33
MSC: Primary 62C15, 62F05, 62M07; Secondary 62B05, 62C07, 60G15
Language: English
Original paper language: Russian
Citation: A. N. Tyulyagin, “On asymptotic admissibility of goodness-of-fit tests”, Izv. Akad. Nauk SSSR Ser. Mat., 46:3 (1982), 569–616; Math. USSR-Izv., 20:3 (1983), 535–576
Citation in format AMSBIB
\Bibitem{Tyu82}
\by A.~N.~Tyulyagin
\paper On asymptotic admissibility of goodness-of-fit tests
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1982
\vol 46
\issue 3
\pages 569--616
\mathnet{http://mi.mathnet.ru/im1627}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=661147}
\zmath{https://zbmath.org/?q=an:0535.62041|0509.62040}
\transl
\jour Math. USSR-Izv.
\yr 1983
\vol 20
\issue 3
\pages 535--576
\crossref{https://doi.org/10.1070/IM1983v020n03ABEH001620}
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    		Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:224
    Russian version PDF:96
    English version PDF:17
    References:37
    First page:1
     
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