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We propose pseudo empirical best linear unbiased estimators of small‐area means based on natural exponential family quadratic variance function models when the basic data consist of survey‐weighted estimators of these means, area‐specific covariates and certain summary measures involving the weights. We also provide explicit approximate mean squared errors of these estimators in the spirit of Prasad & Rao (1990), and these estimators can be readily evaluated. A simulation study is undertaken to evaluate the performance of the proposed inferential procedure. We estimate also the proportion of poor children in the 5–17 years age‐group for the different counties in one of the states in the United States.