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What is Learnable in Valiant's Theory of the Learnable? 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A solution in small area estimation problems
Andrius Čiginas, Tomas Rudys · 2013-06-12 · via math.ST updates on arXiv.org

We present a new method in problems where estimates are needed for finite population domains with small or even zero sample sizes. In contrast to known estimation methods, an auxiliary information is used to model sizes of population units instead of a direct prediction of their values of interest. In particular, via an additional characterization of regression models, we incorporate a scatter and variabilities of the units sizes into an estimator, and then it uses an information of the whole sample by taking into an account a location of the estimation domain inside the population. To reduce an impact of the introduced domain total estimator bias to the mean square error, we construct also a regression type version of the estimator. An efficiency of the method proposed is shown in a simulation study.

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