The general Gauss-Markov model with possibly singular dispersion matrix

Linear models with possibly singular dispersion (variance-covariance) matrix of the vector of disturbances have been considered in the literature since the late sixties. In this paper we give a survey of important results and consequences without a claim to completeness. Proofs are given for the results in Sections 2 to 5. 1 Notation 2 The General Gauss-Markov Model 3 Best Linear Unbiased Estimation 4 Quadratic Unbiased Estimation 5 Testing a Linear Hypothesis 6 Further Aspects of Linear Estimation.