1, English name: the best linear unbiased estimator; ; blue

2. Definition: If the estimator of a parameter is linear (the estimator is a linear function of the sample observation), unbiased (the mathematical expectation of the estimator is equal to the true value) and the variance of the estimation error is the smallest, it is called the best linear unbiased estimator.

3. Applied disciplines: genetics (first-class discipline), population and quantitative genetics (two disciplines)

Extended data

Only the first two statistics (mean, variance and covariance) of unknown parameter X and observation vector Z need to be known in the BLUE estimation. ?

BLUE algorithm is also called linear minimum mean square error estimation (LMMS) because it requires the estimator to have the smallest error in the mean square sense under the linear observation equation.

Related nature—

(1) linear, that is, this estimator is a random variable.

(2) Unbiasedness, that is, the average or expected value E(a) of this estimator is equal to the true value A. ..

(3) It has an effective estimator, that is, this estimator has the smallest variance among all such linear unbiased estimators.