Two Explicit Characterizations of the General Nonnegative-Definite Covariance Matrix Structure for Equality of BLUEs, WLSEs, and LSEs

Phil D. Young, Joshua D. Patrick and Dean M. Young

International Journal of Statistics and Probability, 2020, vol. 9, issue 6, 108

Abstract: We provide a new, concise derivation of necessary and sufficient conditions for the explicit characterization of the general nonnegative-definite covariance structure V of a general Gauss-Markov model with E(y) and Var(y) such that the best linear unbiased estimator, the weighted least squares estimator, and the least squares estimator of Xβ are identical. In addition, we derive a representation of the general nonnegative-definite covariance structure V defined above in terms of its Moore-Penrose pseudo-inverse.

Date: 2020
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