Best Linear Unbiased Estimator
BLUE stands for Best Linear Unbiased Estimator. The phrase comes from the Gauss-markov theorem that the OLS estimator is BLUE when the standard linear regression assumptions (i.e., the errors are independent and identically distributed as a Gaussian with constant variance). The acronym can be broken down as follows:
- An estimator is a specified calculation used on sample data to estimate a quantity (e.g., a population parameter--see also estimators).
- "Unbiased" means that the expected value of the estimator equals the parameter being estimated (conceptually, the sampling distribution of the resulting estimates is centered on the true value--see also unbiased-estimator, and bias).
- "Linear" refers to linear in the parameters.
- "Best" implies that the sampling distribution of the resulting estimates having the lowest variance of all possible unbiased linear estimators.
