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On estimation in hierarchical models with block circular covariance structures

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  • Yuli Liang
  • Dietrich Rosen
  • Tatjana Rosen

Abstract

Hierarchical linear models with a block circular covariance structure are considered. Sufficient conditions for obtaining explicit and unique estimators for the variance–covariance components are derived. Different restricted models are discussed and maximum likelihood estimators are presented. The theory is illustrated through covariance matrices of small sizes and a real-life example. Copyright The Institute of Statistical Mathematics, Tokyo 2015

Suggested Citation

  • Yuli Liang & Dietrich Rosen & Tatjana Rosen, 2015. "On estimation in hierarchical models with block circular covariance structures," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(4), pages 773-791, August.
    • Handle: RePEc:spr:aistmt:v:67:y:2015:i:4:p:773-791
    DOI: 10.1007/s10463-014-0475-8
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    References listed on IDEAS

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    1. Lynn LaMotte, 2007. "A direct derivation of the REML likelihood function," Statistical Papers, Springer, vol. 48(2), pages 321-327, April.
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    Cited by:

    1. Timothy Opheim & Anuradha Roy, 2021. "Linear models for multivariate repeated measures data with block exchangeable covariance structure," Computational Statistics, Springer, vol. 36(3), pages 1931-1963, September.
    2. Katarzyna Filipiak & Mateusz John & Daniel Klein, 2023. "Testing independence under a block compound symmetry covariance structure," Statistical Papers, Springer, vol. 64(2), pages 677-704, April.
    3. Katarzyna Filipiak & Mateusz John & Yuli Liang, 2024. "Testing covariance structures belonging to a quadratic subspace under a doubly multivariate model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(3), pages 847-876, September.
    4. Hao, Chengcheng & Liang, Yuli & Mathew, Thomas, 2016. "Testing variance parameters in models with a Kronecker product covariance structure," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 182-189.
    5. Yuli Liang & Dietrich Rosen & Tatjana Rosen, 2021. "On properties of Toeplitz-type covariance matrices in models with nested random effects," Statistical Papers, Springer, vol. 62(6), pages 2509-2528, December.

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