Gauss–Markov theorem
Teorema de Gauss-Márkov
- Date
- 1821 (Gauss) / 1912 (Markov) · confidence low
- Place
- Göttingen, Germany
- Credited to
- Andrey Markov y Carl Friedrich Gauss
- Field
- Knowledge & symbols
What was discovered
A statistical theorem stating that, in a linear regression model with uncorrelated, homoscedastic, zero-mean errors, the ordinary least squares estimator has the lowest variance among linear unbiased estimators.
Gauss proved a version assuming normality and independence; Markov relaxed the assumptions to the stated form around 1900-1912.
What it led to
- theoretical justification of the least-squares method in statistics and econometrics
- the basis for extensions to non-spherical errors (Aitken)
- a central reference in linear estimation theory
- constant use in applied regression analysis