Unbiased statistical estimation functions for parameters in presence of nuisance parameters (Q791251)

Let X be a random vector with pdf \(p(x;\theta_ 1,\theta_ 2)\), \(\theta_ 1\in R^ r\), \(\theta_ 2\in R^ s\), and let \((X,\theta_ 1)\to g(X,\theta_ 1)\in R^ r\) be an unbiased statistical estimation function (USEF) for estimating \(\theta_ 1\) in the presence of \(\theta_ 2\). Three optimality criteria based on the dispersion matrix of g are discussed, and their equivalence in a class of USEF is established. A Cramér-Rao type inequality is presented.