A Bayesian predictive inference for small area means incorporating covariates and sampling weights

The main goal in small area estimation is to use models to ‘borrow strength’ from the ensemble because the direct estimates of small area parameters are generally unreliable. However, model-based estimates from the small areas do not usually match the value of the single estimate for the large area....

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Bibliographic Details
Published inJournal of statistical planning and inference Vol. 140; no. 11; pp. 2963 - 2979
Main Authors Toto, Ma. Criselda S., Nandram, Balgobin
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier B.V 01.11.2010
Elsevier
Subjects
Exact sciences and technology
General topics
Mathematics
Multivariate normal density
Nested-error regression model
Parametric inference
Posterior propriety
Probability and statistics
Random samples
Sampling theory, sample surveys
Sampling weights
Sciences and techniques of general use
Small area estimation
Statistics
Sampling weights
Posterior propriety
Multivariate normal density
Small area estimation
Nested-error regression model
Random samples
Bayes estimation
Error estimation
Gaussian distribution
Finite population
Statistical decision
Multivariate analysis
Covariate
Statistical simulation
Nested model
Statistical method
Sampling theory
Regression model
Sampling
Sample survey
Posterior distribution
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Summary:The main goal in small area estimation is to use models to ‘borrow strength’ from the ensemble because the direct estimates of small area parameters are generally unreliable. However, model-based estimates from the small areas do not usually match the value of the single estimate for the large area. Benchmarking is done by applying a constraint, internally or externally, to ensure that the ‘total’ of the small areas matches the ‘grand total’. This is particularly useful because it is difficult to check model assumptions owing to the sparseness of the data. We use a Bayesian nested error regression model, which incorporates unit-level covariates and sampling weights, to develop a method to internally benchmark the finite population means of small areas. We use two examples to illustrate our method. We also perform a simulation study to further assess the properties of our method.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2010.03.043