A study of the effects of measurement error in survey sampling

Date
1982
Authors
Chandhok, Promod
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Altmetrics
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Research Projects
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Statistics
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Abstract

The effects of measurement error in survey sampling are investigated. Let y(,jt) be the value of the characteristic under study for the j('th) unit in the population, observed at the t('th) trial. Assume that; y(,jt) = Y(,j) + e(,jt);where Y(,j) is the true value of the j('th) unit, and e(,jt) the deviation from the true value. It is desired to estimate the population mean of y. We study two measurement error models. The first model, called the "simple correlation model," is given by;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI);and; Cov(e(,jt), e(,j't)(VBAR)j, j') = (rho) (sigma)(,j)(sigma)(,j');The second model, called the "intrasample correlation model," is given by;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI);and;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI);for j (NOT=) j', and both j, j' in the sample;The usual unbiased estimators in equal and unequal probability sampling with replacement are studied under the simple correlation model. The Horvitz-Thompson estimator and the simple mean are also examined under the simple correlation model. Some of these estimators are compared in an empirical study;The ratio estimator is studied under two sampling schemes, namely, simple random sampling without replacement and Midzuno's scheme. The bias and mean-square error of the ratio estimator under these two sampling schemes and the two measurement error models are derived and compared. The conditions under which one strategy is better than the other, when measurement error is present, are obtained. Also, the comparison is made in an empirical study;The results are extended to two-stage sampling and stratified sampling.

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