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Scoring with constraints

Published online by Cambridge University Press:  17 February 2009

Michael R. Osborne
Michael R. Osborne
Affiliation:
Centre for Mathematics and its Applications, School of Mathematical Sciences, Australian National University, Canberra, ACT 0200, Australia.
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Abstract

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This paper 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 → ∞, 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 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.

Type
Research Article
Information
The ANZIAM Journal , Volume 42 , Issue 1 , July 2000 , pp. 9 - 25
Copyright
Copyright © Australian Mathematical Society 2000

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