Under the standard linear regression assumptions, the ordinary least squares estimator is the best linear unbiased estimator of the regression coefficients, meaning it has the smallest variance among all linear unbiased estimators. Named for Carl Friedrich Gauss and Andrey Markov, it is the classical justification for least-squares regression.
Facts
StatementIn statistics, the Gauss-Markov theorem (or simply Gauss theorem for some authors) states that the ordinary least squares (OLS) estimator has the lowest sampling variance (variance of the estimator across samples) within the class of linear unbiased estimators, if the errors in the linear regression model are uncorrelated, have equal variances and expectation value of zero. 1 Classification
Statement FormCharacterization Theorem 1 Connections
Sources
1. Gauss-Markov Theorem (Wikipedia)
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In statistics, the Gauss-Markov theorem (or simply Gauss theorem for some authors) states that the ordinary least squares (OLS) estimator has the lowest sampling variance (variance of the estimator across samples) within the class of linear unbiased estimators, if the errors in the linear regression model are uncorrelated, have equal variances and expectation value of zero.
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