Model formulation on efficiency for median estimation under a fixed cost in survey sampling

Abstract

In survey sampling, it is observed that researchers and users of statistics sometimes do not take into consideration the tool that will be most appropriate for the measure of location. As a result, they often go for the mean or total, which has wider coverage in the finite population sampling literature, unlike the median, which is more complicated to deal with given that it has to do with ordered data. Keeping in mind the established facts from the literature on the usefulness of the median estimator in estimating economic indicators for high precision and efficiency, this study has made useful improvement in estimating the population median not only for gains in efficiency but also in achieving less biased estimates. The study suggests an estimator of population median in single and double sampling techniques. In addition, minimum mean square error has also been obtained for a given cost function under double sampling. Results obtained from both theoretical and empirical investigations reveal that the proposed estimators perform better when the considered variables are from a highly skewed distribution, such as income, expenditure, scores, etc. Moreso, it is observed that the proposed estimators compete favorably with less bias and outstanding gains in efficiency than the existing estimators of its class. In addition, this study avails us of an appropriate way of constructing the cost function for better evaluations compared to an existing estimator considered in this work.