Abstract
In a general linear regression model, a generalized least squares estimator (GLSE) is widely employed as an estimator of regression coefficient. The efficiency of the GLSE is usually measured by its covariance (or risk) matrix. In this paper, it is shown that the covariance matrix remains the same as long as the distribution of the error term is elliptically symmetric. This implies that every efficiency result obtained under normal distribution assumption is still valid under elliptical symmetry. An application to a heteroscedastic linear model is also illustrated.
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Kurata, H. A theorem on the covariance matrix of a generalized least squares estimator under an elliptically symmetric error. Stat Papers 51, 389–395 (2010). https://doi.org/10.1007/s00362-009-0199-7
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DOI: https://doi.org/10.1007/s00362-009-0199-7
Keywords
- Linear regression model
- Covariance matrix
- Elliptically symmetric distribution
- Generalized least squares estimator
- Heteroscedastic model