Statistical Inference on Population Proportion in the Presence of Auxiliary attributes: Analysis of Radiation Data

Abstract

Precise estimation of population proportions is a requirement in many disciplines, particularly when direct measurement is difficult, expensive and time consuming. In this paper, we propose a more efficient statistical inference procedure for estimating population proportion in the presence of an auxiliary attributes. The method is applied to an actual radiation dataset with the underlying primary variable considered as the proportion of individuals exposed at a certain threshold value like mean, median, first quartile and third quartile. Comparative study is performed for the proposed estimators with traditional estimators under simple random sampling. Theoretical efficiency of the proposed class of estimators are analyzed and both bias and mean squared error (MSE) expressions are obtained up to the first order of approximation, which has been verified through a comprehensive empirical study. The illustrative radiation data highlight the potential benefit to public health and environmental monitoring of incorporating auxiliary attributes, when good estimates can inform policy and safely standards. This method not only decreases the estimation error, but also provides a cost-efficient counterpart to expensive data collecting schemes. Generally, the study has shown that use of auxiliary attributes in estimation is statistically sound and practically feasible approach to improve the estimates on population proportion, especially in fields such as radiation exposure assessment where there may be inadequacy of sensitive data.