Abstract
The current study deals with imputation of item non-response in probability proportional to size (PPS) sampling. A new imputation procedure is proposed by using the known co-variance between the study variable and the auxiliary variable in the case of quantitative sensitive study variable by considering the non-response in a randomization mechanism on the second call. An empirical study is conducted at the optimum values of kog and nog for the relative comparisons of ratio, difference, and proposed estimators, respectively, with the Hansen-Hurwitz estimator.
Highlights
Survey sampling is a technique which is utilizes in almost every field of life to estimate the finite population parameters with limited response
When units are different in size and variable under study is correlated with their auxiliary information e.g. size, the selection probabilities may be assigned in proportion to their sizes
Y 2Þ2, 1.2 Selection of sample with proportional to size (PPS) sampling In PPS sampling scheme, the selection of units in the sample is carried with probability proportional to a given measure of size, where the size is measured by the available suitable auxiliary information
Summary
Survey sampling is a technique which is utilizes in almost every field of life to estimate the finite population parameters with limited response. If units varying in size, equal probability sampling may not give the appropriate importance to large or small units in the population. When units are different in size and variable under study is correlated with their auxiliary information e.g. size, the selection probabilities may be assigned in proportion to their sizes. 3. In biological studies, the number of patients may be selected according to the size of the hospital. The number of patients may be selected according to the size of the hospital For all of these cases, the selection of sampling units is proportional to the size of auxiliary information associated with the particular unit, is called sampling with probability proportional to size (PPS). In many real life situations, where non-response/refusals may affect the reliability and accuracy of data sets. The detailed discussion on the proposed estimator is given in Subsections 1.1 and 1.2 for the case of simple random and PPS sampling scheme, respectively
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