The interpretation of maximum-likelihood estimation |
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Authors: | David A. Sprott Román Viveros-Aguilera |
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Affiliation: | 1. Department of Statistics and Actuarial Science University of Waterloo Waterloo, Ontario N2L 3G1;2. Escuela de Ciencias Fisico-Matematicas Universidad Autónomu de Puebla Puebla, Mexico |
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Abstract: | Maximum-likelihood estimation is interpreted as a procedure for generating approximate pivotal quantities, that is, functions u(X;θ) of the data X and parameter θ that have distributions not involving θ. Further, these pivotals should be efficient in the sense of reproducing approximately the likelihood function of θ based on X, and they should be approximately linear in θ. To this end the effect of replacing θ by a parameter ϕ = ϕ(θ) is examined. The relationship of maximum-likelihood estimation interpreted in this way to conditional inference is discussed. Examples illustrating this use of maximum-likelihood estimation on small samples are given. |
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Keywords: | Ancillary statistics Bias conditional inference efficiency information linearity pivotal quantities variance |
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