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 CONTACT Tomasz Żądło

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The mean squared error reflects only the average prediction accuracy while the distribution of squared prediction error is positively skewed. Hence, assessing or comparing accuracy based on the MSE (which is the mean of squared errors) is insufficient and even inadequate because we should be interested not only in the average but in the whole distribution of prediction errors. This is the reason why we propose to use different than MSE measures of prediction accuracy in small area estimation. In the prediction accuracy comparisons we take into account our proposal for the empirical best predictor, which is a generalization of the predictor presented by Molina and Rao (2010). The generalization results from the assumption of a longitudinal model and possible changes of the population and subpopulations in time.

Summary This paper presents the problem of prediction of a domain total value based on the general linear model. In many methods presented in the survey sampling literature (e.g. Cassel, Särndal & Wretman, 1977[Foundations of inference in survey sampling, New York: John Wiley & Sons]; Valliant, Dorfman & Royall, 2000[Finite population sampling and inference. A prediction approach. New York: John Wiley & Sons]; Rao, 2003[Small area estimation. New York; John Wiley & Sons]) a common assumption is that for each element of a population the domain to which it belongs is known. This assumption is especially important in the situation when a superpopulation model with auxiliary variables is considered. In this paper a method is proposed for prediction of the domain total when it is not known whether a unit belongs to a given domain or not, or when the information is available only for sampled elements of the population.