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

Abstract

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