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Maximum-likelihood estimators with known incidental parameters

Published online by Cambridge University Press:  24 October 2008

P. A. P. Moran
P. A. P. Moran
Affiliation:
The Australian National University, Canberra
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Suppose we have a sample of N independent random variables X1, …, XN where Xi has the distribution F(X|θ, øi). θ is a k-dimensional ‘structural’ parameter (θ(1), …, θ(k)), and the øi are scalar or vector ‘incidental’ parameters in some given space. The Xi may be scalar or vector random variables which are either discrete in which case we write f(X|θ, øi) for the probability associated with a given point, or else continuous random variables with a probability density f(X|θ, øi). In either case we sup pose the support of the probability distribution to be fixed. We aim to estimate the true value of θ by maximum-likelihood methods.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 72 , Issue 2 , September 1972 , pp. 233 - 241
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

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