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...

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

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

least-squares estimator. An extended version of this result is known as the Gauss–Markov theorem. The idea of least-squares analysis was also independently formulated...

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

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

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...

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...

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"...

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

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

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...

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

Finetti's theorem (probability) FWL theorem (economics) Fieller's theorem (statistics) Fisher–Tippett–Gnedenko theorem (statistics) Gauss–Markov theorem (statistics)...

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...

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

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

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...

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

using Markov chains exist. Dynamics of Markovian particles Gauss–Markov process Markov chain approximation method Markov chain geostatistics Markov chain...

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

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

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

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...

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...

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

equal to the weighted portion of zi which is "explained" by xi. The Gauss–Markov theorem states that regression models which fulfill the classical linear...

possible because the James–Stein estimator is biased, so that the Gauss–Markov theorem does not apply. Similar to the Hodges' estimator, the James-Stein...