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 Izv. Akad. Nauk SSSR Ser. Mat., 1982, Volume 46, Issue 3, Pages 569–616 (Mi izv1627)

On asymptotic admissibility of goodness-of-fit tests

A. N. Tyulyagin

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.

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English version:
Mathematics of the USSR-Izvestiya, 1983, 20:3, 535–576

Bibliographic databases:

UDC: 519.234.33
MSC: Primary 62C15, 62F05, 62M07; Secondary 62B05, 62C07, 60G15

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/izv1627} \mathscinet{http://www.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}