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High-dimensional asymptotic expansion of LR statistic for testing intraclass correlation structure and its error bound

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  • Kato, Naohiro
  • Yamada, Takayuki
  • Fujikoshi, Yasunori

Abstract

This paper deals with the null distribution of a likelihood ratio (LR) statistic for testing the intraclass correlation structure. We derive an asymptotic expansion of the null distribution of the LR statistic when the number of variable p and the sample size N approach infinity together, while the ratio p/N is converging on a finite nonzero limit c[set membership, variant](0,1). Numerical simulations reveal that our approximation is more accurate than the classical [chi]2-type and F-type approximations as p increases in value. Furthermore, we derive a computable error bound for its asymptotic expansion.

Suggested Citation

  • Kato, Naohiro & Yamada, Takayuki & Fujikoshi, Yasunori, 2010. "High-dimensional asymptotic expansion of LR statistic for testing intraclass correlation structure and its error bound," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 101-112, January.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:1:p:101-112
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    References listed on IDEAS

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    1. Fujikoshi, Yasunori & Yamada, Takayuki & Watanabe, Daisuke & Takakazu Sugiyama, 2007. "Asymptotic distribution of the LR statistic for equality of the smallest eigenvalues in high-dimensional principal component analysis," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 2002-2008, November.
    2. James R. Schott, 2005. "Testing for complete independence in high dimensions," Biometrika, Biometrika Trust, vol. 92(4), pages 951-956, December.
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    Cited by:

    1. Kato, Naohiro & Kuriki, Satoshi, 2013. "Likelihood ratio tests for positivity in polynomial regressions," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 334-346.
    2. Klein, Daniel & Pielaszkiewicz, Jolanta & Filipiak, Katarzyna, 2022. "Approximate normality in testing an exchangeable covariance structure under large- and high-dimensional settings," Journal of Multivariate Analysis, Elsevier, vol. 192(C).

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