Gauss–Markov theorem

E29373

result in linear regression theory statistical theorem

The Gauss–Markov theorem is a fundamental result in statistics stating that, under certain conditions, the ordinary least squares estimator is the best linear unbiased estimator (BLUE) of the coefficients in a linear regression model.

Jump to: Statements Referenced by

Statements (47)

Predicate	Object
instanceOf	result in linear regression theory ⓘ statistical theorem ⓘ
abbreviation	BLUE ⓘ
addresses	estimation of regression coefficients ⓘ
appliesTo	linear regression model ⓘ
assumes	exogeneity of regressors ⓘ finite second moments of error terms ⓘ full column rank of the regressor matrix ⓘ homoscedasticity of error terms ⓘ linearity in parameters ⓘ no autocorrelation of error terms ⓘ zero mean error term ⓘ
compares	ordinary least squares estimators ⓘ other linear unbiased estimators ⓘ
concerns	linear unbiased estimators ⓘ ordinary least squares estimator ⓘ
conclusion	ordinary least squares has minimum variance among all linear unbiased estimators ⓘ ordinary least squares is BLUE for the regression coefficients ⓘ
context	classical linear regression model ⓘ
criterion	variance of estimators ⓘ
defines	best linear unbiased estimator ⓘ
doesNotRequire	normality of error terms ⓘ
excludes	biased estimators from its optimality class ⓘ nonlinear estimators from its optimality class ⓘ
field	econometrics ⓘ probability theory ⓘ statistics ⓘ
formalizes	optimality of ordinary least squares under classical assumptions ⓘ
holdsUnder	fixed design matrix assumption ⓘ random design with appropriate conditions ⓘ
implies	ordinary least squares is efficient within the class of linear unbiased estimators ⓘ
motivates	use of ordinary least squares in linear regression ⓘ
namedAfter	Andrei Markov ⓘ surface form: Andrey Markov Carl Friedrich Gauss ⓘ
relatedTo	Cramér–Rao bound ⓘ generalized least squares ⓘ linear minimum variance unbiased estimation ⓘ ordinary least squares method ⓘ
statesThat	under certain assumptions the ordinary least squares estimator is the best linear unbiased estimator of the regression coefficients ⓘ
topicIn	introductory econometrics courses ⓘ mathematical statistics courses ⓘ
typeOfEstimatorClass	linear estimators ⓘ unbiased estimators ⓘ
typeOfOptimality	minimum variance ⓘ
usedIn	applied statistics ⓘ econometric modeling ⓘ time series regression under appropriate conditions ⓘ

Referenced by (2)

Full triples — surface form annotated when it differs from this entity's canonical label.

Carl Friedrich Gauss → hasConceptNamedAfter → Gauss–Markov theorem ⓘ

method of least squares → relatedConcept → Gauss–Markov theorem ⓘ