Constrained Least Squares Estimation and ANOVA

Abstract

In our consideration of least squares estimation up to this point, β was unrestricted, i.e., β could assume any value in $\mathbb {R}^p$. We now consider least squares estimation for models in which β is restricted to the subset of $\mathbb {R}^p$ consisting of all those β-values that satisfy the consistent system of linear equations

$$\displaystyle \mathbf {A}\boldsymbol {\beta } = \mathbf {h}, $$

where A is a specified q × p matrix of rank q ^∗ and h is a specified q-vector.