Improved estimation of the mean through regressed exponential estimators based on sub-sampling non-respondents

The present study concerns the issue of estimating the population mean and presents novel and improved regressed exponential estimators using different parameters of an auxiliary character based on sub-sampling non-respondents. The bias and mean square error (MSE) of the proposed estimators for the most pragmatic simple random sampling without replacement (SRSWOR) scheme have been derived up to the first order of approximation (i.e. the expression containing errors up to the power of two so that the expectation comes only in terms of the mean, variance and covariance). The optimum value of the MSE of the estimators is found, along with the necessary conditions for optimising the MSE. The effectiveness of the suggested estimators, outperforming the existing ones in terms of their MSE, has been studied theoretically, while the empirical as well as the simulation studies have confirmed these findings.