Gauss-Markov_theorem Gauss-Markov theorem From Sterwiki This article is not about Gauss-Markov processes. In statistics, the Gauss-Markov theorem, named after Carl Friedrich Gauss and Andrey Markov, states that in a linear model in which the errors have expectation zero and are uncorrelated and have equal variances, the best linear unbiased estimators of the coefficients are the least-squares estimators. More generally, the best linear unbiased estimator of any linear combination of the coefficients is its least-squares estimator. The errors are not assumed to be normally distributed, nor are they assumed to be independent (but only uncorrelated — a weaker condition), nor are they assumed to be identically distributed (but only homoscedastic — a weaker condition, defined below). More explicitly, and more concretely, suppose we have <math>Y_i=eta_0+eta_1 x_i+varepsilon_i<math> for i = 1, . . ., n, where β0 and β1 are non-random but unobservable parameters, xi are non-random and observable, εi are random, and so Yi are random. (We set x in lower-case because it is not random, and Y in capital because it is random.) The random variables εi are called the 'errors' (not to be confused with 'residuals'; see errors and residuals in statistics). The Gauss-Markov assumptions state that <math>{ m E}left(varepsilon_i ight)=0,<math> <math>{ m var}left(varepsilon_i ight)=sigma^2 Quelle "Gauss-Markov_theorem" : Wikipedia.org Main page for "Gauss-Markov_theorem"