A Comparison of Design‐based and Model‐based Estimators of the Finite Population Distribution Function

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) bas the desirable property from a model-based viewpoint, of being model-unbiased under misspedcation of model, when the sample meets certain conditions. A modified version of this estimator is suggested; it relies lesa 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.

Bias-calibrated Estimation from Sample Surveys Containing Outliers

“…This subpopulation of the beef farm population considered by Dorfman (1993), and Chambers and Kokic (1993) may be described as the population of moderately sized beef farms, where size is interpreted in terms of the number of beef cattle. We consider this subpopulation because the linear model (1.1) holds in it; we intend to treat the nonlinearity exhibited in the full population in subsequent work.…”

Topics in Survey Sampling

“…Also, one could replace Gn(t) in (6.3.7) by a smoother estimator of G, e.g., a kernel estimator of this function, obtained by integrating a kernel density estimator (Hill, 1985). Dorfman (1993) extended CD-estimator to multiple regression model. Dunstan and Chambers (1989) extended CD-estimator to the case where only summary information is available for the auxiliary size variable x.…”

Environmetric analysis in complex surveys

“…Part of the growing literature on the subject is based on the traditional sampling framework such as, for example, the works of Konijn (1962) and Kish and Frankel (1974). Others such as Scott and Holt (1982), Deaton and Irish (1983), King and Evans (1986), Christensen (1984Christensen ( , 1986Christensen ( , 1987a, Moulton (1986Moulton ( , 1990), Dorfman (1993), Rao et al (1993), and more recently, Bhatti (1995Bhatti ( , 1996Bhatti ( , 1997Bhatti ( , 1999 have focused on the model-based approach.…”