Statist. Comput. Simul., 1975, Vol. 3, pp. 283-296
©Gordon and Breach Science Publishers Ltd.
Printed in Great Britain
COMPUTING METHODS FOR LINEAR MODELS
SUBJECT TO LINEAR PARAMETRIC CONSTRAINTS
THOMAS M. GERIG and A. RONALD GALLANT
North Carolina State University, Institute of Statistics,
Raleigh Division Box 5457, Raleigh, North Carolina 27607, U.S.A.
(Received August 21, 1973)
Abstract: An efficient and accurate computational form for which minimizes SSE() = (y - X)' (y- X) subject to R = r using the Moore-Penrose g-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-estimable constraints on the parameters.