Accounting for response missing at random and observed heterogeneity in the estimation of mean: Practice and application to real data of childhood respiratory disease and body fat percentage

An estimate of the mean is required for data analysis and interpretation in all real-world domains, including public health campaigns, clinical and therapeutic decision-making, group response comparison, physiological, medical and pharmaceutical research and other applications. Non-response degrades the statistical power of decision-making in these studies and distorts the generalizability and variability of the research findings due to their random nature. This paper tackles the issue of non-response’s stochastic nature, which poses challenges for researchers attempting to comprehend and regulate study outcome variability. In lieu of that, the key contribution of this study is to develop and acquisition of modified technique of Searls [The utilization of a known coefficient of variation in the estimation procedure, J. Am. Stat. Assoc. 59(308) (1964) 1225–1226, https://doi.org/10.1080/01621459.1964.10480765] optimization along with principle of random non-response to estimate the mean of heterogeneous population. We have also obtained the mathematical expressions for the bias and mean square error [Formula: see text] to characterize the properties of the proposed improved ratio cum exponential estimators, and highlighted the algebraic constraints to strengthen the performance of these estimators. Using statistical packages of R-software, a numerical analysis has been carried out on simulated data and real data sets of childhood respiratory disease and body fat in order to measure the performance of the proposed estimators.