Covariance-Mean Regression Models

Wei Lan and Chih-Ling Tsai
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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

Chapter Chapter 5 in Covariance Analysis and Beyond, 2026, pp 67-81 from Springer

Abstract: 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.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-08796-6_5

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DOI: 10.1007/978-3-032-08796-6_5

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