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Hierarchical Bayes Small Area Estimation under a Unit Level Model with Applications in Agriculture

Author(s)
Nageena Nazir Division of Agri-statistics, SKUAST-K, Shalimar, India.
Shakeel Ahmad Mir Division of Agri-statistics, SKUAST-K, Shalimar, India
M Iqbal Jeelani Division of Agri-statistics, SKUAST-K, Shalimar, India
Abstract
To studied Bayesian aspect of small area estimation using Unit level model. In this paper we proposed and evaluated new prior distribution for the ratio s 2 /s e2 (= l ) of variance components in unit level model v rather than uniform prior. To approximate the posterior moments of small area means, Laplace approximation method is applied. This choice of prior avoids the extreme skewness, usually present in the posterior distribution of variance components. This property leads to more accurate Laplace approximation. We apply the proposed model to the analysis of horticultural data and results from the model are compared with frequestist approach and with Bayesian model of uniform prior in terms of average relative bias, average squared relative bias and average absolute bias. The numerical results obtained highlighted the superiority of using the proposed prior over the uniform prior. Thus Bayes estimators (with new prior) of small area means have good frequentist properties such as MSE and ARB as compared to other traditional methods viz., Direct, Synthetic and Composite estimators.
Publication Details
Page(s) 491-506
DOI DOI not available
Published Journal: Pakistan Journal of Statistics and Operation Research, Volume: 12, Issue: 3, Year: 2016

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Keywords
Small Area Estimation, Unit Level Model, Hierarchical Bayes
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