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Gauss-Markov theorem (4849 bytes)
1: ''This article is '''not''' about [[Gauss-Markov process]]es.'' 5: In [[statistics]], the '''[[Gauss-Markov]] theorem''', named after [[Carl Friedrich Gauss]] and [[An... 11: ... [[errors and residuals in statistics]]). The '''Gauss-Markov''' assumptions state that 42: ... the matrix algebra formulation, the Gauss-Markov theorem shows that the difference between the parameter c... 46: ...www.xycoon.com/ols1.htm Proof of the Gauss Markov theorem for multiple linear regression] (makes use of mat... Gauss-Markov (570 bytes) 1: The phrase '''Gauss-Markov''' is used in two different ways. See 2: *[[Gauss-Markov process]]es in [[probability theory]]. 3: *The [[Gauss-Markov theorem]] in mathematical [[statistics]]. 4: A major point of the latter theorem is that one does '''not''' assume the probability... 6: The second sense of "Gauss-Markov" is far more widely known than the first because ... Gauss-Markov process (1762 bytes) 1: ...his article is '''not''' about the [[Gauss-Markov theorem]] of mathematical [[statistics]].'' 5: As one would expect, '''[[Gauss-Markov]] stochastic processes''' (named after [[Carl Fri... 7: Every Gauss-Markov process ''X''(''t'') possesses the three followin... 9: ...''Z''(''t'') = ''h''(''t'')''X''(''t'') is also a Gauss-Markov process 10: ...then ''Z''(''t'') = ''X''(''f''(''t'')) is also a Gauss-Markov process Gauss-Bonnet theorem (1571 bytes) 1: ...ich Gauss|Gauss]]-[[Pierre Ossian Bonnet|Bonnet]] theorem''' in [[differential geometry]] is an important s... 7: The theorem applies in particular if the manifold does not ha... 9: ...e, while the curvatures at given points will. The theorem requires, somewhat surprisingly, that the 12: ...en Chern|Chern]]. See [[generalized Gauss-Bonnet theorem]] and [[Chern-Weil homomorphism]]. 14: [[Category:Riemannian geometry]][[Category:Theorems]] Generalized Gauss-Bonnet theorem (1353 bytes) 1: ...is a direct generalization of the [[Gauss-Bonnet theorem]] to general even dimension. 5: The '''generalized-Gauss-Bonnet theorem''' states that 10: As with the Gauss-Bonnet theorem, there are generalizations when ''M'' is a [[mani... Markov (233 bytes) Markov blanket (512 bytes) Markov algorithm (1853 bytes) Georgi Markov (2108 bytes) Frantisek Markov (939 bytes) Andrey Markov (1961 bytes) 7: * [[Gauss-Markov theorem]] 13: * A.A. Markov. "Extension of the limit theorems of probability theory to a sum of variables conn... Markov (crater) (1872 bytes) Markov chain (10048 bytes) 109: ...</math>. This is stated by the [[Perron-Frobenius theorem]]. 135: * A.A. Markov. "Extension of the limit theorems of probability theory to a sum of variables conn... Markov network (1008 bytes) Markov property (2155 bytes) Causal Markov Condition (298 bytes) Examples of Markov chains (5358 bytes) Hidden Markov model (4155 bytes) Markov's inequality (2216 bytes) 12: ...d expectations, that are all examples of a single theorem. 14: ===Theorem=== 25: The theorem follows by taking the expectation of both sides o... 33: ...ng a lower bound, that are along the lines of the theorem presented here, but those might best be saved for... Markov decision process (762 bytes)
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