MoonJung Cho and John L. Eltinge " Identification of Functional Forms and Predictor Variables in Generalized Variance Functions for Price Indices"

Generalized variance functions (GVFs) can provide useful approximations of error variances, especially for complex-survey cases in which (1) standard variance estimators have insufficient degrees of freedom for direct use, (2) confidentiality restrictions prevent the release of design information used in direct variance estimation, or (3) computational time requirements may be incompatible with short timelines for publication of estimates. Much of the GVF literature has considered variances of estimators for population proportions, and used population totals and sample sizes as predictors in the resulting variance-function models. Some surveys, however, have variance-estimation settings that meet criteria (1), (2) or (3) above, but involve point estimators that are complex nonlinear functions of the data. This paper derives the functional forms and predictors for a GVF in this setting; applies the results to a class of price-index estimators; and evaluates the properties of the resulting GVFs.