Some Results on Parameter Estimation in Linear Models With Prior Information

Consider the linear model Y=Xβ+e; e～N(0, σ~2I). (1) where X is a known n×p matrix of rank p<n; β∈R~p and σ>0 are parameters. Assume that prior information about β in the form U=Hβ+ε (2) is available. Here H is a known k×p matrix. and H≠0; ε～N(0, W); W is known and positive definite symmetric. Assume also that e and ε are independent.