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Small Area Estimation with a Multivariate Spatial-Temporal Model

Year: 2012       Vol.: 61       No.: 2      

Authors: Arturo M. Martinez, Jr

Abstract:

A multivariate generalization of a spatial-temporal is postulated and used in model-based small area estimation where small area information is borrowed from other units through spatial and temporal correlations. An estimation procedure that combined the backfitting algorithm, AR-sieve bootstrap and Lorenz curve parameterization is proposed. The procedure is illustrated using data on mean per capita income quintiles of households in the Philippines with provincial unit of analysis. The generation of unit-record synthetic household income is feasible even if modeling is done at the provincial level. Estimates of poverty indices based on the synthetic unit-record data generated from the multivariate spatial-temporal model are more reliable than the direct survey estimates. There are only small deviations between the model-based and direct survey estimates of poverty indices at the domain level that validates the accuracy of the model-based small area estimates generated from the multivariate spatial-temporal model.

Keywords: backfitting algorithm; AR-sieve bootstrap; Lorenz curve parameterization; poverty index

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