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Modelling structured correlation matrices

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  • Ruey S. Tsay
  • Mohsen Pourahmadi

Abstract

SUMMARY Ensuring positive definiteness of an estimated structured correlation matrix is challenging. We show that reparameterizing Cholesky factors of correlation matrices using hyperspherical coordinates or angles provides a flexible and effective solution. Once a structured correlation matrix is identified, the corresponding angles and hence the constrained correlations may be estimated by maximum likelihood. Consistency and asymptotic normality of the maximum likelihood estimators of the angles are established. Examples demonstrate the flexibility of the method.

Suggested Citation

  • Ruey S. Tsay & Mohsen Pourahmadi, 2017. "Modelling structured correlation matrices," Biometrika, Biometrika Trust, vol. 104(1), pages 237-242.
    • Handle: RePEc:oup:biomet:v:104:y:2017:i:1:p:237-242.
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    File URL: http://hdl.handle.net/10.1093/biomet/asw061
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    References listed on IDEAS

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    1. Creal, Drew & Koopman, Siem Jan & Lucas, André, 2011. "A Dynamic Multivariate Heavy-Tailed Model for Time-Varying Volatilities and Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(4), pages 552-563.
    2. Weiping Zhang & Chenlei Leng & Cheng Yong Tang, 2015. "A joint modelling approach for longitudinal studies," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(1), pages 219-238, January.
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    Cited by:

    1. Christopher J. Urban & Daniel J. Bauer, 2021. "A Deep Learning Algorithm for High-Dimensional Exploratory Item Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 1-29, March.
    2. Saxena, Shobhit & Bhat, Chandra R. & Pinjari, Abdul Rawoof, 2023. "Separation-based parameterization strategies for estimation of restricted covariance matrices in multivariate model systems," Journal of choice modelling, Elsevier, vol. 47(C).
    3. Kuang‐Yao Lee & Lexin Li, 2022. "Functional structural equation model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 600-629, April.

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