Estimation of Domain Mean under Two Stage Sampling with Units Missing at Random
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Authors
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Kaustav Aditya
ICAR-Indian Agricultural Statistics Research Institute, New Delhi
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Bharti
ICAR-Indian Agricultural Statistics Research Institute, New Delhi
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Safeela Nasrin
ICAR-Indian Agricultural Statistics Research Institute, New Delhi
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Shrila Das
Keywords:
Random response; Missing at random; Sub-sampling; Cost function, Domain estimation, Two stage sampling.Abstract
Estimation of domain means is crucial in large-scale surveys; however, it becomes difficult when some of the selected units fail to respond. Sub
sampling of non-respondents serves as a practical and methodologically sound approach to address this issue. This study considers the estimation of
domain mean under a random response mechanism using a two-stage sampling design with two phases at the second stage. Three estimators were
developed based on sub-sampling of non-respondents, where additional effort was made to collect information from a selected sub-sample. Variance
expressions were obtained for each estimator, and the optimum sample sizes were determined by minimizing the expected cost for a given level of
precision. The empirical analysis shows a considerable reduction in expected cost for all proposed estimators, with the highest reduction observed
when nonresponse is minimum. The study concludes that the proposed estimators are more efficient and cost-effective for domain mean estimation
when nonresponse is present.
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