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Biometrika 1993 80(4):905-909; doi:10.1093/biomet/80.4.905
© 1993 by Biometrika Trust
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MISCELLANEA

Unbiased estimating equations derived from statistics that are functions of a parameter

D. R. COX

Nufield College Oxford, OX1 1NF, U. K.

The formation of a combination of the observed random variables and a parameter of interest {psi} having a distribution depending only on {psi} provides one approach to the analysis of problems with many nuisance parameters. The condition for the resulting formal maximum likelihood estimating equation for {psi} to be unbiased is derived. Applications include a regression model for exponentially distributed random variables with errors in the explanatory variables.

Key Words: Errors in explanatory variables • Estimating equation • Functional relation • Incidental parameter • Score function • Structural relation


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