Abstract
This paper describes theoretical estimation of domains mean using double sampling with a non-linear cost function in the presence of non-response. The estimation of domain mean is proposed using auxiliary information in which the study and auxiliary variable suffers from non-response in the second phase sampling. The expression of the biases and mean square errors of the proposed estimators are obtained. The optimal stratum sample sizes for given set of non-linear cost function are developed.
Highlights
Domain is a subgroup of the whole target population of the survey for which specific estimates are needed
According to Sahoo and Panda [10] if an experimenter knows the population mean of an additional auxiliary variable, say, Z whereas the population mean of an auxiliary variable X is unknown and can be estimated using double sampling scheme, it is possible to come up with a class of estimators for the finite population mean μY
The expression for the Mean square error (MSE) of YdR1 and YdR2 are derived by the use of the Taylor's series approximation
Summary
Domain is a subgroup of the whole target population of the survey for which specific estimates are needed. Estimates are made in each of the class into which the population is subdivided; for instance, the focus may be the unemployment rate of the entire population and the break-down by age, gender and education level. Units of domains may sometimes be identified prior to sampling. In such cases, the domains can be treated as separate stratum from a specific sample taken. Stratification ensures a satisfactory level of representativeness of the domains in the final sample.
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