Springer Texts in Business and Economics
Efficiency as Correlation. This is based on Zheng (1994)
3.12 Since " and " are linear unbiased estimators of ", it follows that" C X(" — ") for any X is a linear unbiased estimator of ". Since " is the BLU estimator of ",
2 var
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is minimized at X — 0. Setting the derivative of var " C X(" — ") respect to X at X — 0, we have 2E " (" — ") — 0, or E("2) — E(""). Thus, the squared correlation between " and " is
r(") var (") var(") var(") var(") ’
where the third equality uses the result that E("2) — E(""). The final equality gives var(")/var(") which is the relative efficiency of " and ".
