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An Introduction to Model-Based Survey Sampling with Applications$
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Ray Chambers and Robert Clark

Print publication date: 2012

Print ISBN-13: 9780198566625

Published to Oxford Scholarship Online: May 2012

DOI: 10.1093/acprof:oso/9780198566625.001.0001

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Prediction for Small Areas

Prediction for Small Areas

Chapter:
(p.161) 15 Prediction for Small Areas
Source:
An Introduction to Model-Based Survey Sampling with Applications
Author(s):

Raymond L. Chambers

Robert G. Clark

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198566625.003.0015

Prediction for small areas introduces an important application of sample survey inference, where domain sample sizes are too small to allow domain-specific inference. Typically, these domains are spatially defined, and so are referred to as small areas. Direct and indirect estimation for small areas is discussed, with the latter based on characterising the distribution of the survey variable via a linear mixed model. The empirical best linear unbiased predictor is developed, as are estimates of its mean squared error. An alternative approach, which conditions on differences between the areas, is used to motivate a domain-type linear estimator, the model-based direct estimator, as well as an estimator of its conditional mean squared error. The extension of the indirect approach to where the survey variable can be modelled via a generalised linear mixed model is sketched. The chapter concludes with a discussion of recent developments in small area inference

Keywords:   small area estimation, direct estimation, indirect estimation, empirical best linear unbiased predictor, mean squared error estimation, model-based direct estimation, empirical best prediction

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