An optimality criterion for vector unbiased statistical estimation functions (Q1115053)

The author and \textit{B. K. Kale} [ibid. 9, 45-54 (1984; Zbl 0535.62030)] considered the problem of estimating a vector interesting parameter in the presence of nuisance parameters through vector unbiased statistical estimation functions (USEFs) and obtained an extension of the Cramér- Rao inequality. Based on this result, three optimality criteria were proposed and their equivalence was established. In this paper, motivated by the uniformly minimum risk criterion [see \textit{S. Zacks}, The theory of statistical inference. (1971), p. 102] for estimators, we propose a new optimality criterion for vector USEFs in the nuisance parameter case and show that it is equivalent to the three existing criteria.