On the correct discrimination of Gaussian hypotheses. II.
Rovskiĭ, V.A. (2004)
Zapiski Nauchnykh Seminarov POMI
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Rovskiĭ, V.A. (2004)
Zapiski Nauchnykh Seminarov POMI
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Renze, John, Wagon, Stan, Wick, Brian (2001)
Experimental Mathematics
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Ion Vladimirescu, Radu Tunaru (2003)
Commentationes Mathematicae Universitatis Carolinae
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The aim of this article is to develop estimation functions by confidence regions for the inverse Gaussian distribution with two parameters and to construct tests for hypotheses testing concerning the parameter when the mean parameter is known. The tests constructed are uniformly most powerful tests and for testing the point null hypothesis it is also unbiased.
H. Luschgy (1991)
Metrika
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Dinh, Khoan T., Nguyen, Nhu T., Nguyen, Truc T. (2003)
International Journal of Mathematics and Mathematical Sciences
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Manfred G. Madritsch (2008)
Acta Arithmetica
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Tadeusz Inglot, Alicja Janic (2009)
Applicationes Mathematicae
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We construct a new class of data driven tests for uniformity, which have greater average power than existing ones for finite samples. Using a simulation study, we show that these tests as well as some "optimal maximum test" attain an average power close to the optimal Bayes test. Finally, we prove that, in the middle range of the power function, the loss in average power of the "optimal maximum test" with respect to the Neyman-Pearson tests, constructed separately for each alternative,...
Elliot H. Lieb (1990)
Inventiones mathematicae
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Yuichi Futa, Hiroyuki Okazaki, Daichi Mizushima, Yasunari Shidama (2013)
Formalized Mathematics
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Gaussian integer is one of basic algebraic integers. In this article we formalize some definitions about Gaussian integers [27]. We also formalize ring (called Gaussian integer ring), Z-module and Z-algebra generated by Gaussian integer mentioned above. Moreover, we formalize some definitions about Gaussian rational numbers and Gaussian rational number field. Then we prove that the Gaussian rational number field and a quotient field of the Gaussian integer ring are isomorphic. ...
Nathan Keller, Elchanan Mossel, Arnab Sen (2014)
Annales de l'I.H.P. Probabilités et statistiques
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In a recent paper, we presented a new definition of influences in product spaces of continuous distributions, and showed that analogues of the most fundamental results on discrete influences, such as the KKL theorem, hold for the new definition in Gaussian space. In this paper we prove Gaussian analogues of two of the central applications of influences: Talagrand’s lower bound on the correlation of increasing subsets of the discrete cube, and the Benjamini–Kalai–Schramm (BKS) noise sensitivity...