On the performance of small-area estimators: fixed vs. random area parameters

• Autores: Alex Costa, Albert Satorra Brucart , Eva Ventura Colera
• Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 33, Nº. 1, 2009, págs. 85-104
• Idioma: inglés
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• Resumen

  • Most methods for small-area estimation are based on composite estimators derived from design- or model-based methods. A composite estimator is a linear combination of a direct and an indirect estimator with weights that usually depend on unknown parameters which need to be estimated. Although model-based small-area estimators are usually based on random-effects models, the assumption of fixed effects is at face value more appropriate. Model-based estimators are justified by the assumption of random area effects; in practice, however, areas can not be substituted for one another in a random manner (we say, they are not interchangeable). In the present paper we empirically assess the quality of several small-area estimators in the setting in which the area effects are treated as fixed. We consider two settings: one that draws samples from a theoretical population, and another that draws samples from an empirical population of a labour force register maintained by the National Institute of Social Security (NISS) of Catalonia. We distinguish two types of composite estimators: a) those that use weights that involve area specific estimates of bias and variance; and, b) those that use weights that involve a common variance and a common squared bias estimate for all the areas. We assess their precision and discuss alternatives to optimizing composite estimation in applications.

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