Survey sampling and small-area estimation

Abstract

This issue is devoted to survey sampling methods. It carries on a tradition of Mathematical Population Studies, after the issues guest-edited by Malay Ghosh and Tomasz Ża̧dło (2014) and Vera Toepoel and Schonlau (2017). Wright (2001) presented some major moments of the history of survey sampling. He acknowledged the pioneering work of Pierre Simon de Laplace (1878-1912; Gillispie, 1997), who estimated the population size of France in 1802 based on a sample of communes, which were administrative districts. He multiplied the population size of the sampled communes by the ratio of the recorded total number of births for the whole country to the one recorded in the sample. He used the same method to estimate the population size of France for 1782. John Graunt (1665) had also used a similar calculus to estimate the population size of England in 1662. In design-based inference, introduced by Neyman (1934), the values taken by the variable of interest are considered as fixed and the sampling design is the only source of randomness affecting the estimates. In modelbased inference, the values taken by the variable of interest are considered as the realizations of random variables. The set of conditions defining the class of this distribution is called “super-population” model (Cassel et al., 1976: 80) and inference is made conditionally on the sample, which is either drawn at random or chosen purposively from the population. Accuracy is measured only over possible realizations of the variables. In model-assisted inference, the model is used to increase accuracy, but good design-based properties, such as design consistency, are of primary interest. Various methods include calibration estimators and pseudo-empirical best linear unbiased predictors. The accuracy of the former is evaluated through randomization techniques; the accuracy of the latter through a model. In the Bayesian framework, the estimator is a conditional expectation in the posterior distribution of the population or subpopulation parameters and the posterior variance is used as a measure of the variability of the Bayesian estimator. This Bayesian technique applies to continuous, binary, and count data.