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.
Keywords
MathematicsLikelihood functionEstimatorApplied mathematicsScore testAsymptotic distributionLikelihood-ratio testEstimating equationsEstimation theoryLikelihood principleRestricted maximum likelihoodMaximum likelihoodLagrange multiplierM-estimatorStatisticsMathematical optimizationQuasi-maximum likelihood
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Publication Info
- Year
- 1958
- Type
- article
- Volume
- 29
- Issue
- 3
- Pages
- 813-828
- Citations
- 588
- Access
- Closed
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Cite This
J. Aitchison,
S. D. Silvey
(1958).
Maximum-Likelihood Estimation of Parameters Subject to Restraints.
The Annals of Mathematical Statistics
, 29
(3)
, 813-828.
https://doi.org/10.1214/aoms/1177706538
Identifiers
- DOI
- 10.1214/aoms/1177706538