Variance Estimation in Finite Population Sampling

Abstract

Under a linear regression model, the best linear unbiased estimator (BLUE) for a finite population total can be obtained. The problem studied here is that of estimating the variance for setting large-sample confidence intervals about the BLUE when the model generating this estimate is inaccurate. A robust variance estimator is derived, and its asymptotic properties are shown to compare favorably with those of the weighted least-squares variance estimator. The robust variance estimator is shown to be asymptotically equivalent to the jackknife variance estimator under rather general conditions. These are extensions of results previously established for the ratio estimator by Royall and Eberhardt (1975).

Key Words:

• Robust variance estimator
• Sampling theory
• Superpopulation models
• Linear prediction
• Jackknife
• Balanced sample