In statistics, the Gauss–Markov theorem (or simply Gauss theorem for some authors) states that the ordinary least squares (OLS) estimator has the lowest...

The phrase Gauss–Markov is used in two different ways: Gauss–Markov processes in probability theory The Gauss–Markov theorem in mathematical statistics...

Gauss–Markov process Gauss–Markov theorem Gaussian copula Gaussian measure Gaussian correlation inequality Gaussian isoperimetric inequality Gauss's inequality...

distribution. The central limit theorem supports the idea that this is a good approximation in many cases. The Gauss–Markov theorem. In a linear model in which...

residuals when regressors have finite fourth moments and—by the Gauss–Markov theorem—optimal in the class of linear unbiased estimators when the errors...

Andrey Markov Chebyshev–Markov–Stieltjes inequalities Gauss–Markov theorem Gauss–Markov process Hidden Markov model Markov blanket Markov chain Markov decision...

estimators under the assumption of normally distributed errors (Gauss–Markov theorem), in the two-part paper Theoria combinationis observationum erroribus...

Gauss–Markov theorem Gauss–Markov process Markov blanket Markov boundary Markov chain Markov chain central limit theorem Additive Markov chain Markov...

uncorrelatedness of errors, and if one still assumes zero mean, then the Gauss–Markov theorem entails that the solution is the minimal unbiased linear estimator...

S}{\partial \beta _{j}}}({\hat {\boldsymbol {\beta }}})=0} . The Gauss–Markov theorem shows that, when this is so, β ^ {\displaystyle {\hat {\boldsymbol...

matrix and show that it is positive definite. This is provided by the Gauss–Markov theorem. Linear least squares methods include mainly: Ordinary least squares...

of zero and a constant variance, σ {\displaystyle \sigma } , the Gauss–Markov theorem states that the least-squares estimator, β ^ {\displaystyle {\hat...

inequality Fefferman's inequality Fréchet inequalities Gauss's inequality Gauss–Markov theorem, the statement that the least-squares estimators in certain...

biased estimates as it violates the exogeneity assumption of the Gauss–Markov theorem. The problem of endogeneity is often ignored by researchers conducting...

under the conditions of the Gauss–Markov theorem. The least-squares method was published in 1805 by Legendre and in 1809 by Gauss. The first design of an...

errors. When OLS is used on data with homoscedastic errors, the Gauss–Markov theorem applies, so the GLS estimate is the best linear unbiased estimator...

{\boldsymbol {u}}} , respectively. This is a consequence of the Gauss–Markov theorem when the conditional variance of the outcome is not scalable to the...

Erdős–Ko–Rado theorem Euler's formula Euler's four-square identity Euler's theorem Five color theorem Five lemma Fundamental theorem of arithmetic Gauss–Markov theorem...

exact linear relationship. Contrary to popular belief, neither the Gauss–Markov theorem nor the more common maximum likelihood justification for ordinary...

process Gamma variate GAUSS (software) Gauss's inequality Gauss–Kuzmin distribution Gauss–Markov process Gauss–Markov theorem Gauss–Newton algorithm Gaussian...

regression, the use of the least-squares estimator is justified by the Gauss–Markov theorem, which does not assume that the distribution is normal. From the...

geostatistics Markov chain mixing time Markov chain tree theorem Markov decision process Markov information source Markov odometer Markov operator Markov random...

analysis) Gauss–Markov theorem (statistics) Gauss–Wantzel theorem (geometry) Gelfand–Mazur theorem (Banach algebra) Gelfand–Naimark theorem (functional...

minor planets). Gauss published a further development of the theory of least squares in 1821, including a version of the Gauss–Markov theorem. The term "regression"...

^{\mathsf {T}}\ \Delta \mathbf {y} .} These equations form the basis for the Gauss–Newton algorithm for a non-linear least squares problem. Note the sign convention...

loss function. Best linear unbiased estimator, also known as the Gauss–Markov theorem states that the ordinary least squares (OLS) estimator has the lowest...

is no heteroscedasticity. Breaking this assumption means that the Gauss–Markov theorem does not apply, meaning that OLS estimators are not the Best Linear...

assumption that the error terms are uncorrelated, meaning that the Gauss Markov theorem does not apply, and that OLS estimators are no longer the Best Linear...

unbiased estimator based on assumptions on covariances, make use of Gauss–Markov theorem to prove independence of the estimate and error, and use very similar...

effects are similar to best linear unbiased estimates (BLUEs) (see Gauss–Markov theorem) of fixed effects. The distinction arises because it is conventional...