Small area estimation under informative probability sampling of areas and within the selected areas


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), 1427-1439. (doi:10.1198/016214507000001094).

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Description/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.

Item Type: Article
ISSNs: 0162-1459 (print)
1537-274X (electronic)
Keywords: body mass index, bootstrap, design based inference, sample distribution, sample-complement distribution, sampling weights
Subjects: H Social Sciences > HA Statistics
Divisions: University Structure - Pre August 2011 > Southampton Statistical Sciences Research Institute
ePrint ID: 48099
Date Deposited: 28 Aug 2007
Last Modified: 27 Mar 2014 18:31
Contact Email Address: msdanny@soton.ac.uk
URI: http://eprints.soton.ac.uk/id/eprint/48099

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