Open Conference Systems, ITACOSM 2019 - Survey and Data Science

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Using the Entropic Distance for Large Area Definition in Small Area Estimation Methods
Fabrizio Solari, Livio Fenga

Building: Learning Center Morgagni
Room: Aula Magna 327
Date: 2019-06-05 04:20 PM – 06:00 PM
Last modified: 2019-05-23


As it is well-known, small area estimation methods rely on the specification of a proper statistical model, which is applied to the overall area (e.g. country, region, etc.) resulting from the aggregation of the full set of the small areas (e.g. country, region, etc.). However, often the related model assumptions fail to be satisfied. As a result, bias components can arise.

In order to minimize this bias component, a double step approach is commonly followed, i.e.: the partition of the overall area into a set of large areas, each one resulting by aggregating a subset of all the available small areas, is performed (first step). Then, distinct models are applied to each large area (second step). Often, the choice of such a partition is based on administrative reasons. Of course, more efficient results can be reasonably expected, when the choice of the large areas is data driven instead of determined by mere administrative criteria.

When small area data from several periods of time are available, we propose a time dependent-based approach to aggregate small areas in larger areas. In essence, we employ an entropy defined distance function to assess the similarity of the trajectories over time followed by  the small area time series. The method has proved to be fast, effective and flexible. The latter characteristic is important, as it allows the analysts to calibrate the desired similarity level according to the specificity of the data set at hand.

Our approach to define a suitable set of large areas is compared with standard criteria by means of an experimental study. To this end, the 2004-2014 Italian Labour Force Survey data will be considered to define an ad hoc large area for each single small area. Then, standard and spatial Fay-Herriot models are used to assess the properties of the aforementioned large areas. Furthermore, a spatio-temporal Fay-Herriot will be used in order to borrow strength also from time.

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