The Annals of Mathematical Statistics

Maximum-Likelihood Estimation of Parameters Subject to Restraints

J. Aitchison and S. D. Silvey

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Math. Statist., Volume 29, Number 3 (1958), 813-828.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177706538

Digital Object Identifier
doi:10.1214/aoms/1177706538

Mathematical Reviews number (MathSciNet)
MR94873

Zentralblatt MATH identifier
0092.36704

JSTOR
links.jstor.org

Citation

Aitchison, J.; Silvey, S. D. Maximum-Likelihood Estimation of Parameters Subject to Restraints. Ann. Math. Statist. 29 (1958), no. 3, 813--828. doi:10.1214/aoms/1177706538. https://projecteuclid.org/euclid.aoms/1177706538


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