Some measures of robustness for unbiased estimators in one-parameter natural exponential families with quadratic variance function

In this paper two measures to highlight the possible effect of an observation on the UMVU estimate are proposed. Our study is based in expansions in terms of orthogonal polynomials for the UMVUE when sampling from a NEF-QVF. We obtain the conditional bias and the asymptotic mean sensitivity curve (AMSC) for the UMVUE. We observe that these measures depend on parametric function under consideration at the true and unknown value of the parameter. We study in detail their properties and relationships as well as to the Hampel’s influence function. In fact, we note that the AMSC also verifies for the UMVUE in the NEF-QVF some of most relevant properties of influence function. Also a case-deletion influence diagnostic and some simulations are included to illustrate our results. © 2007 Elsevier Inc. All rights reserved