When a Mean-of-Ratios is the Best Linear Unbiased Estimator under a Model

This article sheds some revealing light on a commonly used design-based estimation strategy that nonetheless remains a mystery to many users.A simple regression model is introduced that is slightly different from the one frequently studied in the model-based literature.Starting with this model and a particular error structure, a simple mathematical trick is employed to show that a mean-of-ratios (Horvitz-Thompson) estimator based on a .-balanced sample is the best linear unbiased estimation strategy.Extensions follow.