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...

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

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...

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...

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

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

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"...

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

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...

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...

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

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...

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

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

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...

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

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

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

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...

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

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

variance. Accuracy and precision Bias of an estimator Double descent Gauss–Markov theorem Hyperparameter optimization Law of total variance Minimum-variance...

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

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...

the minimum-variance linear unbiased estimator, according to the Gauss–Markov theorem. The term λ n I {\displaystyle \lambda nI} therefore leads to a biased...

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...

Regression validation Mean and predicted response Errors and residuals Goodness of fit Studentized residual Gauss–Markov theorem Mathematics portal v t e...