Estimating Function Jackknife Variance Estimators Under Stratified Multistage Sampling

Abstract

Generalized regression (GREG) uses auxiliary variables with known population totals to improve efficiency of estimators and to ensure consistency with the known totals. Variance estimation for the GREG estimator of a total under stratified multistage sampling is considered. Customary resampling methods (jackknife, balanced repeated replication and bootstrap) for estimating the variance of a GREG estimator require the inversion of a P × P matrix for each resample, where P is the number of auxiliary variables with known population totals. This could lead to illconditioned matrices for some of the resamples. We apply the estimating function (EF) resampling method of Hu and Kalbfleisch [Hu, F., Kalbfleisch, J. D. (2000). The estimating function bootstrap (with discussion). Can. J. Statist. 28:449–499] to obtain variance estimators, using jackknife resampling. This method avoids repeated inverses. We extend the results to cover parameters defined as solutions of census estimating equations. The proposed method can be implemented from micro data files containing the GREG weights and the associated EF jackknife weights.

Key Words:

• Census estimating equation
• Generalised regression estimator
• Jackknife

Mathematics Subject Classification:

• Primary 62D05
• Secondary 62G09

Acknowledgment

This work was supported by a grant from the Natural Sciences and Engineering Research Council of Canada.