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Bounds for the trace of the difference of the covariance matrices of the OLSE and BLUE. (English) Zbl 0753.62033
Summary: In the linear model \(\{y,X\beta,V\}\), the inefficiency of the ordinary least squares estimator of \(X\beta\) can be measured as the difference of the covariance matrices of the ordinary least squares estimator and the best linear unbiased estimator of \(X\beta\). C. R. Rao [ibid. 70, 249-255 (1985; Zbl 0594.62073)] gave an upper bound for the trace of this difference, assuming that the covariance matrix \(V\) is positive definite. In this paper, we generalize this result to the situation when \(V\) is allowed to be singular.

MSC:
62H12 Estimation in multivariate analysis
62J05 Linear regression; mixed models
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