Small-area estimation with spatial similarity
N.T. Longford
Abstract
Small-area estimation is gaining importance in official statistics
as clients of national statistical agencies demand more and more
detailed information about the country, its regions (states) and
smaller geographical units. Surveys can rarely be designed so that
they would contain sufficient direct information about every one of
the units, especially when their sizes are disparate. Small-area estimation addresses this problem by applying models that assess
the extent of similarity and exploit the similarity the units.
A class of composite estimators of small-area quantities
that exploit spatial (distance-related) similarity is introduced.
They are based on a distribution-free model for the areas,
but the estimators are aimed to have optimal design-based properties.
Composition is applied also to estimating some of the global parameters
on which the small-area estimators depend.
The commonly adopted assumption of random effects
is not necessary for exploiting the similarity of the districts
(borrowing strength across the districts).
The methods are applied to estimation of the mean household sizes
and the proportions of single-member households in the counties
(comarcas) of Catalonia.
In Computational Statistics and Data Analysis 54, 2010.