Linear Model

Abstract

Let X be an n×u matrix of given coefficients with full column rank, i.e. rankX = u, β a u × 1 random vector of unknown parameters, y an n × 1 random vector of observations, D(y|σ²) = σ²P^-1 the n× n covariance matrix of y, σ² the unknown random variable which is called variance factor or variance of unit weight and P the known positive definite weight matrix of the observations. Then $X\beta = E(y|\beta ){\mathbf{ }}with{\mathbf{ }}D(y|\sigma ^2 ) = \sigma ^2 P^{ - 1} {\mathbf{ }}$ is called a linear model.