A best linear unbiased estimator, usually shortened to BLUE, is a linear unbiased estimator that has the smallest variance among all linear unbiased estimators in the class being considered.
What each word means
- Best: lowest variance in the relevant class
- Linear: built as a linear function of the observed data
- Unbiased: centered on the true parameter in expectation
In introductory econometrics, the famous statement is that ordinary least squares is BLUE under the Gauss-Markov assumptions.
Why the idea matters
BLUE is about efficiency within a restricted class. It does not mean an estimator is perfect, and it does not automatically mean it is best among all possible nonlinear estimators. It means that, given linearity and unbiasedness, no other estimator in that class is more precise.
Model logic
The concept matters because empirical work balances several estimator properties at once:
- unbiasedness,
- variance,
- consistency,
- robustness to assumption failures.
BLUE clarifies one important benchmark: what OLS can achieve when the classical linear-model assumptions hold.