Scoring With Constraints

Research Report MRR95-035

Scoring With Constraints

Michael R. Osborne

Abstract: This report considers the solution of estimation problems based on the maximum likelihood principle when a fixed number of equality constraints are imposed on the parameters of the problem. Consistency and the asymptotic distribution of the parameter estimates are discussed as $n\rightarrow\infty$ , where n is the number of independent observations, and it is shown that a suitably scaled limiting multiplier vector is known. It is shown that when this information is available then the good properties of Fisher's method of scoring 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.

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