Computing methods for linear models subject -to linear parametric constraints

An efficient and accurate computational form for p which minimizes SSE(fi) = (y— Xfi)’ (y — Xfi) subject to Rfi — r using the Moore-Penrose ^-inverse is given. No rank conditions are imposed on R or X. The results are applied (i) to estimate the parameters in a linear model which are subject to linear equality constraints and (ii) to obtain the generalized inverse of X'X which yields a solution of the normal equations subject to non-estimabie constraints on the parameters.