From Equivalent Linear Equations to Gauss-Markov Theorem

The Gauss-markov Theorem and Spurious Regressions

The purpose of this paper is to study the exact nite sample properties of estimators and test statistics for regression coeÆcients of spurious regressions with unit root nonstationary variables. The conditional probability version of the Gauss-Markov theorem is used to nd eÆcient estimators. Then with an additional assumption that the error is normally distributed conditional on the regressors,...

The Use of the Gauss–markov Theorem in Winds Analysis*

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Regularization and the General Gauss-markov Linear Model

If the coefficient matrix in the general Gauss-Markov linear model is ill-conditioned, then the solution is very sensitive to perturbations. For such problems, we propose to add Tikhonov regularization to the model, and we show that this actually stabilizes the solution and decreases its variance. We also give a numerically stable algorithm for computing the regularized solution efficiently.

Isotropic Gauss - Markov Currents *

A natural definition of the Markov property for multi-parameter random processes (random fields) is the following. Let {Xt, tEIR N} be a multiparameter process. For any set D in N. N, let a D denote the a-field generated by {Xt, tED}. The field {Xt, tEN. u} is said to be Markov (or Markov of degree 1 [6], or sharp Markov) if, for any bounded open set D with smooth boundary, oD and ape are condi...

The Gauss-Bonnet Theorem