Machine Learning: BLUE Estimator (Linear Regression)

Rahul S
2 min readSep 6, 2023

BLUE estimator” in the context of linear regression stands for “Best Linear Unbiased Estimator.”

  1. Best: The term “Best” signifies that the BLUE estimator is selected to be the best among all possible linear estimators in a specific sense. Specifically, it aims to minimize the variance of the parameter estimates. In simpler terms, it tries to find the parameter estimates that have the smallest spread or uncertainty while maintaining certain important properties.
  2. Linear: The BLUE estimator is linear because it involves linear combinations of the observed data or predictors. In linear regression, you assume that the relationship between the dependent variable (the one you’re trying to predict) and the independent variables (predictors) is linear. The coefficients in front of these predictors are what you’re estimating, and these coefficients are linear in nature.
  3. Unbiased: The BLUE estimator is unbiased, which means that, on average, it provides parameter estimates that are equal to the true population values. In other words, if you were to use the BLUE estimator on many different samples from the same population, the average of the estimates would converge to the actual population parameter values.

In linear regression, OLS is a commonly used BLUE estimator. It finds the coefficients that minimize the sum of the squared differences between the observed and predicted values of the dependent variable.