Scoring with constraints

This paper considers the solution of estimation problems based on the maxim um likelihood principle when a fixed number of equality constraints are imp osed on the parameters of the problem. Consistency and the asymptotic distr ibution of the parameter estimates are discussed as n --> infinity, where n is the number of independent observations, and it is shown that a suitably scaled limiting multiplier vector is known. It is also shown that when thi s information is available then the good properties of Fisher's method of s coring for the unconstrained case extend to a class of augmented Lagrangian methods for the constrained case. This point is illustrated by means of an example involving the estimation of a mixture density.