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Teoriya Veroyatnostei i ee Primeneniya, 2023, Volume 68, Issue 4, Pages 705–718
DOI: https://doi.org/10.4213/tvp5644 (Mi tvp5644) 		 
Laplace expansion for Bartlett–Nanda–Pillai's test statistic and its error bound

H. Wakakia, V. V. Ulyanovbc

a Graduate School of Advanced Science and Engineering, Hiroshima University, Higashi-Hirosima, Japan
b Lomonosov Moscow State University
c HSE University, Moscow
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DOI: https://doi.org/10.4213/tvp5644
Abstract: We construct asymptotic expansions for the distribution function of the Bartlett–Nanda–Pillai statistic under the condition that the null linear hypothesis is valid in a multivariate linear model. Computable estimates of the accuracy of approximation are obtained via the Laplace approximation method, which is generalized to integrals for matrix-valued functions.
Keywords: Bartlett–Nanda–Pillai statistics, nonasymptotic analysis, Laplace approximation method.
Funding agency Grant number
Japan Society for the Promotion of Science JP17K000519
HSE Basic Research Program
Received: 12.03.2023
Accepted: 18.09.2023
English version:
Theory of Probability and its Applications, 2024, Volume 68, Issue 4, Pages 570–581
DOI: https://doi.org/10.1137/S0040585X97T991635
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: H. Wakaki, V. V. Ulyanov, “Laplace expansion for Bartlett–Nanda–Pillai's test statistic and its error bound”, Teor. Veroyatnost. i Primenen., 68:4 (2023), 705–718; Theory Probab. Appl., 68:4 (2024), 570–581
Citation in format AMSBIB
\Bibitem{WakUly23}
\by H.~Wakaki, V.~V.~Ulyanov
\paper Laplace expansion for Bartlett--Nanda--Pillai's test statistic and its error bound
\jour Teor. Veroyatnost. i Primenen.
\yr 2023
\vol 68
\issue 4
\pages 705--718
\mathnet{http://mi.mathnet.ru/tvp5644}
\crossref{https://doi.org/10.4213/tvp5644}
\transl
\jour Theory Probab. Appl.
\yr 2024
\vol 68
\issue 4
\pages 570--581
\crossref{https://doi.org/10.1137/S0040585X97T991635}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85185281063}
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  • https://www.mathnet.ru/eng/tvp/v68/i4/p705
    • This publication is cited in the following 1 articles:
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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