Completeness and optimality of marginal likelihood estimating equations

Abstract

A counter-example shows that the proof of optimality of the marginal likelihood estimating function for parameter of interest, under the conditions assumed in Lloyd (1987), contains a gap and is, thus, invalid. The same comment applies to the generalized version of Lloyd’s Theorem given by Bhapkar and Srinivasan (1993). In the light of known results concerning Fisher information for parameter of interest and partial sufficiency of a suitable statistic, the counter-example reveals a similar gap in the proof of corollary 3.2 of Bhapkar (1991).