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

In mathematics the Markov theorem gives necessary and sufficient conditions for two braids to have closures that are equivalent knots or links. The conditions...

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

the need to use the Markov chain central limit theorem when estimating the error of mean values. These algorithms create Markov chains such that they...

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

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

A Markov number or Markoff number is a positive integer x, y or z that is part of a solution to the Markov Diophantine equation x 2 + y 2 + z 2 = 3 x y...

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

In mathematics, the Riesz–Markov–Kakutani representation theorem relates linear functionals on spaces of continuous functions on a locally compact space...

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

processes, the Markov chain central limit theorem has a conclusion somewhat similar in form to that of the classic central limit theorem (CLT) of probability...

mathematical theory of Markov chains, the Markov chain tree theorem is an expression for the stationary distribution of a Markov chain with finitely many...

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

classes of nonnegative matrices. This theorem has important applications to probability theory (ergodicity of Markov chains); to the theory of dynamical...

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

represented as events generated by a Markov network (also known as a Markov random field). It is the fundamental theorem of random fields. It states that...

In mathematics, the Markov–Kakutani fixed-point theorem, named after Andrey Markov and Shizuo Kakutani, states that a commuting family of continuous affine...

particular associated with Markov's principle and Markov's rule in mathematical logic, Markov's theorem in knot theory and Markov algorithm in theoretical...

the theory of least squares in 1821, including a version of the Gauss–Markov theorem. The term "regression" was coined by Francis Galton in the 19th century...

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

\mathbb {Z} } . In modern sources, the Adyan–Rabin theorem is usually stated as follows: Let P be a Markov property of finitely presentable groups. Then there...

unbiased estimators of the coefficients, under the conditions of the Gauss–Markov theorem. The least-squares method was published in 1805 by Legendre and in 1809...

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....

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 estimator...

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

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

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 perspective...

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...

A continuous-time Markov chain (CTMC) is a continuous stochastic process in which, for each state, the process will change state according to an exponential...