Small area estimation under informative probability sampling of areas and within the selected areas
Small area estimation under informative probability sampling of areas and within the selected areas
In this article we show how to predict small area means and obtain valid MSE estimators and confidence intervals when the areas represented in the sample are sampled with unequal probabilities that are possibly related to the true (unknown) area means, and the sampling of units within the selected areas is with probabilities that are possibly related to the outcome values. Ignoring the effects of the sampling process on the distribution of the observed outcomes in such cases may bias the inference very severely. Classical design based inference that uses the randomization distribution of probability weighted estimators cannot be applied for predicting the means of nonsampled areas. We propose simple test statistics for testing the informativeness of the selection of the areas and the sampling of units within the selected areas. The proposed procedures are illustrated by a simulation study and a real application of estimating mean body mass index in counties of the U.S.A, using data from the NHANES III survey.
body mass index, bootstrap, design based inference, sample
distribution, sample-complement distribution, sampling weights
1427-1439
Pfeffermann, Danny
c7fe07a0-9715-42ce-b90b-1d4f2c2c6ffc
Sverchkov, Michail
425615f0-784c-4e6f-8108-2c50e1f4cb42
12 November 2007
Pfeffermann, Danny
c7fe07a0-9715-42ce-b90b-1d4f2c2c6ffc
Sverchkov, Michail
425615f0-784c-4e6f-8108-2c50e1f4cb42
Pfeffermann, Danny and Sverchkov, Michail
(2007)
Small area estimation under informative probability sampling of areas and within the selected areas.
Journal of the American Statistical Association, 102 (480), .
(doi:10.1198/016214507000001094).
Abstract
In this article we show how to predict small area means and obtain valid MSE estimators and confidence intervals when the areas represented in the sample are sampled with unequal probabilities that are possibly related to the true (unknown) area means, and the sampling of units within the selected areas is with probabilities that are possibly related to the outcome values. Ignoring the effects of the sampling process on the distribution of the observed outcomes in such cases may bias the inference very severely. Classical design based inference that uses the randomization distribution of probability weighted estimators cannot be applied for predicting the means of nonsampled areas. We propose simple test statistics for testing the informativeness of the selection of the areas and the sampling of units within the selected areas. The proposed procedures are illustrated by a simulation study and a real application of estimating mean body mass index in counties of the U.S.A, using data from the NHANES III survey.
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Pfeffermann_Sverchkov.pdf
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Submitted date: August 2007
Published date: 12 November 2007
Keywords:
body mass index, bootstrap, design based inference, sample
distribution, sample-complement distribution, sampling weights
Identifiers
Local EPrints ID: 48099
URI: http://eprints.soton.ac.uk/id/eprint/48099
ISSN: 0162-1459
PURE UUID: 98ee8f0b-635b-4fab-8248-7844ec4f3f29
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Date deposited: 28 Aug 2007
Last modified: 15 Mar 2024 09:43
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Author:
Michail Sverchkov
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