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<p>Under the multivariate model with partitioned vector of observations various estimators of a block covariance matrix with structured cross-covariance matrices are proposed. It is assumed that the structure of the off-diagonal block of the covariance matrix corresponds to the appropriate part of autoregression of the order one structure, AR(1). The maximum likelihood and least squares estimators are determined and four new estimators are proposed. Comparison of estimates using simulation studies and real data example is demonstrated, respectively. The simulation studied suggested that maximum likelihood and intuitive estimates have the best statistical properties and the latter are computationally simple.</p>

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Block covariance matrix estimation with structured off-diagonal blocks

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月23日

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  • Monika Mokrzycka,
  • Malwina Mrowińska

摘要

Under the multivariate model with partitioned vector of observations various estimators of a block covariance matrix with structured cross-covariance matrices are proposed. It is assumed that the structure of the off-diagonal block of the covariance matrix corresponds to the appropriate part of autoregression of the order one structure, AR(1). The maximum likelihood and least squares estimators are determined and four new estimators are proposed. Comparison of estimates using simulation studies and real data example is demonstrated, respectively. The simulation studied suggested that maximum likelihood and intuitive estimates have the best statistical properties and the latter are computationally simple.