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Covariance-Mean Regression Models

In: Covariance Analysis and Beyond

Author

Listed:
  • Wei Lan

    (Southwestern University of Finance and Economics, School of Statistics and Data Science and Center of Statistical Research)

  • Chih-Ling Tsai

    (University of California - Davis, Graduate School of Management)

Abstract

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.

Suggested Citation

  • Wei Lan & Chih-Ling Tsai, 2026. "Covariance-Mean Regression Models," Springer Books, in: Covariance Analysis and Beyond, chapter 0, pages 67-81, Springer.
    • Handle: RePEc:spr:sprchp:978-3-032-08796-6_5
    DOI: 10.1007/978-3-032-08796-6_5
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