Use of functionals in linearization and composite estimation with application to two-sample survey data

• 成果类型: Article
• 署名作者: Goga, C.; Deville, J-C.; Ruiz-Gazen, A.
• 署名单位: Universite Bourgogne Europe; Ecole Nationale de la Statistique et de l'Analyse de l'Information (ENSAI); Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asp039
• 发表日期: 2009
• 页码: 691709

摘要

An important problem associated with two-sample surveys is the estimation of nonlinear functions of finite population totals such as ratios, correlation coefficients or measures of income inequality. Computation and estimation of the variance of such complex statistics are made more difficult by the existence of overlapping units. In one-sample surveys, the linearization method based on the influence function approach is a powerful tool for variance estimation. We introduce a two-sample linearization technique that can be viewed as a generalization of the one-sample influence function approach. Our technique is based on expressing the parameters of interest as multivariate functionals of finite and discrete measures and then using partial influence functions to compute the linearized variables. Under broad assumptions, the asymptotic variance of the substitution estimator, derived from Deville (1999), is shown to be the variance of a weighted sum of the linearized variables. The paper then focuses on a general class of composite substitution estimators, and from this class the optimal estimator for minimizing the asymptotic variance is obtained. The efficiency of the optimal composite estimator is demonstrated through an empirical study.