Jackknife Variance Estimation under Imputation for Estimators Using Poststratification Information

Abstract

Poststratified estimators are commonly used in sample surveys to improve the efficiency of estimators and to ensure calibration to known poststrata counts. Similarly, generalized regression estimators are used to handle two or more poststratifiers with known marginal counts. In addition, weighting adjustment within weighting classes is used to handle unit nonresponse, and imputation within imputation classes is used to handle item nonresponse. For the full response case, asymptotic consistency of the jackknife variance estimator under stratified multistage sampling is established using mild regularity conditions on “residuals” similar to those of Scott and Wu for ratio and regression estimation under simple random sampling. A jackknife linearization variance estimator, obtained by linearizing the jackknife variance estimator, is also given. For unit nonresponse, the general case of poststrata cutting across weighting classes is considered, and a jackknife variance estimator and the corresponding jackknife linearization variance estimator are obtained. For item nonresponse, weighted mean imputation and weighted hot deck stochastic imputation within imputation classes are studied. Jackknife variance estimators, based on “adjusted” imputed values, are proposed, and the corresponding jackknife linearization variance estimators are obtained. Asymptotic consistency of the jackknife variance estimator is established for both the unit and item nonresponse cases under mild conditions on “residuals,” assuming uniform response within classes. Simulation results for the poststratified estimator under weighted mean imputation and weighted hot deck stochastic imputation are presented.

Key Words:

• Adjusted imputed values
• Generalized regression estimator
• Jackknife linearization variance estimator
• Poststratified estimator
• Stratified multistage sampling