Jackknife Bias-Corrected Generalized Regression Estimator in Survey Sampling

The generalized regression (GREG) estimator is a well-known procedure for using auxiliary data to estimate means or totals using a sample selected from a finite population. The GREG estimator is motivated by an assumed linear superpopulation model and it is known to be asymptotically unbiased regardless of whether the model is correctly specified or not. When the sample size is small and/or when the linear model does not fit the sample data well, the GREG estimator may have nonnegligible bias. In this article, we use the jackknife procedure to correct the bias of the GREG. We evaluate, both theoretically and by simulation, the performance of the jackknife bias-corrected regression estimator (GREG-JK) under unistage sampling without replacement with unequal probabilities. A jackknife mean squared error (MSE) estimator is proposed that naturally includes a finite population correction, which is usually absent in the standard jackknife methods for variance estimation. A simulation study shows that the empirical bias of GREG-JK is negligible for all sample sizes and generated populations. Furthermore, the proposed jackknife MSE estimator demonstrates improvements over the customary estimator.