| Abstract: | Rival estimators of the distribution function of a finite population, derived from the model-based and design-based approaches to sampling inference, are compared. A design-based estimator due to Rao, Kovar & Mantel (1990) has the desirable property from a model-based viewpoint, of being model-unbiased under misspecification of model, when the sample meets certain conditions. A modified version of this estimator is suggested; it relies less on design-based ingredients, and in particular avoids second-order inclusion probabilities. It is the preferred estimator when, as is often the case in sampling practice, the model is adopted without thorough consideration of goodness of fit. However, if standard regression procedures of model construction and criticism are employed, then a strictly model-based estimator does better. |
