Survey weighted estimating equation inference with nuisance functionals

This paper provides a rigorous treatment on design-based estimating equation inference using complex survey data in the presence of nuisance functionals. The proposed design-based framework covers parameters from inequality measures and measures on performance evaluation in economic, business and financial studies but the scope of the paper is more broad. Unlike nuisance parameters in other settings where profile analysis is commonly used, the nuisance functionals are typically handled by using a “plug-in” estimator. We establish root-n consistency and asymptotic normality for parameters defined through survey weighted smooth or non-differentiable estimating functions even if the “plug-in” estimator for the nuisance functional has a convergence rate slower than root-n. A multiplier bootstrap procedure is proposed for three types of commonly used survey designs to tackle the challenge task of variance estimation. Results from a simulation study and an application to a real survey data set demonstrate the effectiveness of the proposed design-based inference on the Lorenz curve.