A Note on Variance Estimation for the Regression Estimator in Double Sampling

Double sampling of a finite population occurs when a sample from the population is itself sampled, with the intent of measuring varites in the subsample not already available in the sample. An important example is the regression estimator for means or totals, which uses values of an auxiliary variable from the full sample to estimate the mean of a variable of interest that is available only on the subsample. This article concerns estimation of the variance of the regression estimator. The estimators of variance recommended by Cochran rely solely on the subsample data, at least to first order. This article note proposes variance estimators that make better use of the entire sample.