Journal of Official Statistics, Vol.14, No.2, 1998. pp. 181–188

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Bias Correction in the Balanced-half-sample Method if the Number of Sampled Units in Some Strata Is Odd

The balanced-half-sample method is a general method for estimating variances of statistics based on complex sample surveys. A simple extension of this method to the case of more than two sampled units in some strata is the grouping method. The sampled units in a stratum are randomly grouped into two equal or nearly equal groups and the balanced-half-sample method is applied to these groups. If all strata have an even number of sampled units, then for linear estimators this grouping method results in unbiased variance estimators, otherwise it results in biased variance estimators. For simple linear estimators an analytical formula for’this bias is derived. It turns out that this bias can be reduced by an appropriate location transformation of the target and auxiliary variable observations.

BHS method; grouping method; location transformation; variance estimation; regression estimator.

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