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This chapter first reviews the four known mean regression models with non-spherical (non-identity) covariance matrices: weighted regression, generalized least squaresGeneralized least squares, longitudinal dataLongitudinal data, and multivariate regression. These models lead us to then introduce covariance-mean regression models. The theoretical properties of regression parameter estimators are established. In addition, two test statistics are presented: one analyzes the necessity of the auxiliary information, and the other assesses the adequacy of the covariance-mean regression model. Two examples are presented to briefly illustrate empirical applications.

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Covariance-Mean Regression Models

  • 章节

  • 发表日期：

    2026年

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  • Wei Lan,
  • Chih-Ling Tsai

摘要

This chapter first reviews the four known mean regression models with non-spherical (non-identity) covariance matrices: weighted regression, generalized least squaresGeneralized least squares, longitudinal dataLongitudinal data, and multivariate regression. These models lead us to then introduce covariance-mean regression models. The theoretical properties of regression parameter estimators are established. In addition, two test statistics are presented: one analyzes the necessity of the auxiliary information, and the other assesses the adequacy of the covariance-mean regression model. Two examples are presented to briefly illustrate empirical applications.