Abstract
Studies have been carried out on domain mean estimation using non-linear cost function. However little has been done on domain stratum estimation using non-linear cost function using ratio estimation in the presence of non-response. This study develops a method of optimal stratum sample size allocation in domain mean estimation using double sampling with non-linear cost function in the presence of non- response. To obtain an optimum sample size, Lagrangian multiplier technique is employed by minimizing precision at a specified cost. In the estimation of the domain mean, auxiliary variable information in which the study and auxiliary variables both suffers from non-response in the second phase sampling is used. The expressions of the biases and mean square errors of proposed estimator has also been obtained.
Highlights
In sampling, estimates are made in each of the class into which the population is subdivided
In double sampling when the problem of American Journal of Theoretical and Applied Statistics 2018; 7(2): 45-57 non-response is present, the strata are virtually divided into two disjoint and exhaustive groups of respondents and nonrespondents
In developing the concept of domain theory with nonresponse the following assumptions are made; i. Both the domain study and auxiliary variables suffers from non-response
Summary
Estimates are made in each of the class into which the population is subdivided. Such subgroups or classes are known as the domain of study. Units of domains may sometimes be identified prior to sampling. For unplanned domain the units cannot be identified prior to sampling and the estimates of certain domains is often evident only after the sampling design has been identified or after the Sampling and field work have been completed. According to Eurostat [4] the precision threshold and or minimum effective sample sizes are set up for effective planned domains. The population value Yd and 2 yd is unknowns and have to be estimated using data from auxiliary sources
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