Estimation of unknown parameters of linear regression in the presence of prior information (Q1177771)

Let \(y=\sum_{k=1}^ n\theta_ k x_ k+\xi\) be a regression model, where \(y\in H\) (\(H\) a real, separable Hilbert space), \(x_ k\in H\), \(k=1,\dots,n\); \(\theta=(\theta_ 1,\dots,\theta_ n)'\) is a random vector of unknown parameters with mean \(A_ \beta\) and correlation matrix \(K\), \(A\) is a known real matrix and \(\xi\in H\) is a random element with mean \(E \xi=0\). The problem of estimating the vectors \(\theta\) and \(\beta\) is considered. The a priori information has the form: \(\beta\in\Lambda_ i\), where \(\Lambda_ i\) are some sets.