On Prediction of Totals for Domains Defined by Random Attributes
The problem of prediction of domain totals is widely discussed in the small area estimation literature (e.g. Rao 2003). In the classic approach it assumed that the population is divided into disjoint domains and sum of domains gives the whole set of population elements. In this paper we define random variables which realizations inform if the i-th population element has the attribute d (belongs to the d-th random domain). What is more, one population element may have no attribute or more than one attribute. The proposed model may be treated as the model assuming random overlapping domains. We present the problem of prediction of a domain total (or being more precise - total value for element of population with some attributes) based on the general linear mixed model (GLMM). Different model (assuming inter alia that one population element may belong at random only to one of domains) was considered by Żądło (2006). The main aim of this paper is to present the equation of the best linear unbiased predictor (BLUP) and its mean squared error (MSE) under the proposed model. Additionally the problem of estimation of model parameters will be studied and its influence on the predictor's accuracy will be considered in the simulation study. (original abstract)
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