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September, 1958 Maximum-Likelihood Estimation of Parameters Subject to Restraints
J. Aitchison, S. D. Silvey
Ann. Math. Statist. 29(3): 813-828 (September, 1958). DOI: 10.1214/aoms/1177706538


The estimation of a parameter lying in a subset of a set of possible parameters is considered. This subset is the null space of a well-behaved function and the estimator considered lies in the subset and is a solution of likelihood equations containing a Lagrangian multiplier. It is proved that, under certain conditions analogous to those of Cramer, these equations have a solution which gives a local maximum of the likelihood function. The asymptotic distribution of this `restricted maximum likelihood estimator' and an iterative method of solving the equations are discussed. Finally a test is introduced of the hypothesis that the true parameter does lie in the subset; this test, which is of wide applicability, makes use of the distribution of the random Lagrangian multiplier appearing in the likelihood equations.


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J. Aitchison. S. D. Silvey. "Maximum-Likelihood Estimation of Parameters Subject to Restraints." Ann. Math. Statist. 29 (3) 813 - 828, September, 1958.


Published: September, 1958
First available in Project Euclid: 27 April 2007

zbMATH: 0092.36704
MathSciNet: MR94873
Digital Object Identifier: 10.1214/aoms/1177706538

Rights: Copyright © 1958 Institute of Mathematical Statistics

Vol.29 • No. 3 • September, 1958
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