Calibration Estimation in Survey Sampling

Abstract

Calibration estimation, where the sampling weights are adjusted to make certain estimators match known population totals, is commonly used in survey sampling. The generalized regression estimator is an example of a calibration estimator. Given the functional form of the calibration adjustment term, we establish the asymptotic equivalence between the functional-form calibration estimator and an instrumental variable calibration estimator where the instrumental variable is directly determined from the functional form in the calibration equation. Variance estimation based on linearization is discussed and applied to some recently proposed calibration estimators. The results are extended to the estimator that is a solution to the calibrated estimating equation. Results from a limited simulation study are presented.

Population empirical likelihood for nonparametric inference in survey sampling

“…The resulting SEL estimator is algebraically equivalent to the nonparametric likelihood estimator proposed by Kim (2009). Furthermore, under certain conditions, it can be shown that…”

“…Chen and Sitter (1999) considered the pseudo empirical likelihood estimator that uses the sampling weight in the empirical log-likelihood function. Kim (2009) considered an alternative empirical likelihood function based on the biased sampling likelihood of Vardi (1985) and Qin (1993). In either case, the resulting empirical likelihood estimator naturally incorporates the available population information and achieves optimality under some limited situations.…”

Reweighting the General Household Survey 1979–2007

“…The non-response factors are applied before raking, which is carried out using Calmar 11,12,13,14,15 . Related to the specific question of the efficiency of using a combination of household and individual level characteristics rather than individual weights, we can refer to the study by Lemaître and Dufour 16 , who conclude that their preliminary results 'suggest that individual and family estimation could be integrated at little or no loss in efficiency for estimates of persons'.…”

A Further Study of Propensity Score Calibration in Missing Data Analysis

“…Estimators in Tan (2006;, Qin and Zhang (2007), Kim (2009;, Chan (2012), Han and Wang (2013), Chan and Yam (2014) and Tan and Wu (2015) are convex combinations of the observed outcomes, and thus always fall within the range of observed values, known as sample boundedness property (Robins et al 2007). …”

“…Nice properties of these estimators mainly rely on delicate construction of augmentation terms and/or careful estimation of data distribution parameters. In recent literature, many researchers proposed to use weight derived by modifying the raw propensity score (Tan 2006(Tan , 2010Qin and Zhang 2007;Chen, Leung and Qin 2008;Qin, Shao and Zhang 2008;Kim 2009Kim , 2010Chan 2012;Han and Wang 2013;Chan and Yam 2014;Han 2014aHan , 2014bTan and Wu 2015;Han 2016).…”