What is it about?
Researchers and users of statistics often use mean or total as a tool for the measures of location that serves as a summary of the data without considering the distribution of the data set and the level of precision which the representative value of such data set is derived. The choice of using 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 have often resulted in misleading results. Keeping this in mind and the facts from the literature on the usefulness of the median estimator in estimating economic indicators for high precision and efficiency, this study has made some improvements in estimating the population median not only for gains in efficiency but also in achieving reliable estimates with less bias. This study suggests estimators of population median in single and double sampling techniques from the class of exponential estimators by adjusting the weights. In addition, a minimum mean square error has also been obtain 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. The proposed estimators have performed creditably well against the existing ones of its class in terms of bias and gains in efficiency. This study has further availed us of an appropriate way of constructing the cost function for better evaluations compared to an existing estimator considered in this work, and the suggested estimators would be preferred for estimating the population median in two-phase sampling for more gains in efficiency with a minimum cost. Consequently, it suffices to conclude that the proposed estimator will be suitable and highly recommended when the variable under study has a skewed distribution.
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Why is it important?
This work has created a pathway for using a median estimator in estimating population parameters in survey sampling to obtain reliable estimates at a minimum cost. I have constructed weights that yielded fruitful results against other existing estimators of its class. Most importantly. I have formulated a cost function which agrees with the theory and design of two-phase sampling with outstanding performance.
Perspectives
I do not doubt that this article will go a long way in educating researchers and users of statistics on the right tool to be used when considering variables of skewed data. In an analysis consisting of economic indicators such as income, expenditure, scores, etc, where we are confronted with outliers, it becomes important to choose an appropriate tool for the measures of location such as the proposed estimators. Again, trying to construct weights that yielded an asymptotic unbiased estimator gives me great pleasure as it has bridged the gap between a less biased estimator and a smaller mean square error. Unarguably, the formulation of the cost function in this work has given a facelift to the work and direction to users of statistics to avoid misleading results.
MATTHEW ISEH
Akwa Ibom State University
Read the Original
This page is a summary of: Model formulation on efficiency for median estimation under a fixed cost in survey sampling, Model Assisted Statistics and Applications, December 2023, IOS Press,
DOI: 10.3233/mas-231437.
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