Does the model matter for GREG estimation? A business survey example

Although asymptotically design-unbiased, GREG estimators may produce bad estimates. The article examines the behaviour of GREG estimators when the underlying models are misspecified. It shows how an efficient GREG estimator was found for a business survey that posed some problems. The work involved data exploration in several steps, combined with analyses of g-weights, residuals and standard regression diagnostics. We discuss two diagnostics for whether a GREG estimate is reasonable or not. A common justification for the use of GREG estimators is that, being asymptotically design unbiased, they are relatively robust to model choice. However, we show that the property of being asymptotically design unbiased is not a substitute for a careful model specification search, especially when dealing with the highly variable and outlier prone populations that are the focus of many business surveys.