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Tests for the existence of group effects and interactions for two-way models with dependent errors

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Abstract

In this paper, we propose tests for the existence of random effects and interactions for two-way models with dependent errors. We prove that the proposed tests are asymptotically distribution-free which have asymptotically size \({{\tau }}\) and are consistent. We elucidate the nontrivial power under the local alternative when a sample size tends to infinity and the number of groups is fixed. A simulation study is performed to investigate the finite-sample performance of the proposed tests. In the real data analysis, we apply our tests to the daily log-returns of 24 stock prices from six countries and four sectors. We find that there is no strong evidence to support the existence of substantial differences in the log-return across countries, nor to the existence of interactions between countries and sectors. However, there exists random effect differences in the daily log-return series across different sectors.

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Acknowledgements

The authors are grateful to the editor and referee for their instructive comments.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Faculty of Mathematics, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

    Yuichi Goto

  2. Department of Pure and Applied Mathematics, Graduate School of Fundamental Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan

    Kotone Suzuki

  3. Department of Probability and Statistics, Wuhan University, 299 Ba Yi Road, Wuchang District, Wuhan, 430072, Hubei, People’s Republic of China

    Xiaofei Xu

  4. Faculty of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan

    Masanobu Taniguchi

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  1. Yuichi Goto
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  2. Kotone Suzuki
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  3. Xiaofei Xu
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  4. Masanobu Taniguchi
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Correspondence to Xiaofei Xu.

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This research was supported by JSPS Grant-in-Aid for Research Activity Start-up under Grant Number JP21K20338 (Y.G.); JSPS Grant-in-Aid for Scientific Research (S) under Grant Number JP18H05290 (M.T.); the Research Institute for Science & Engineering (RISE) of Waseda University (M.T.). Y.G’s research was mainly carried out when he was affiliated with Waseda University. X.X’s research was done while she was visiting the RISE of Waseda University.

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Goto, Y., Suzuki, K., Xu, X. et al. Tests for the existence of group effects and interactions for two-way models with dependent errors. Ann Inst Stat Math 75, 511–532 (2023). https://doi.org/10.1007/s10463-022-00853-3

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  • DOI: https://doi.org/10.1007/s10463-022-00853-3

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