The study proposed an alternative imputation scheme for the schemes which converged to sample mean as the values of unknown parameters in their estimators converged to zero. The estimator of the population means for the proposed scheme as well as the bias and MSE were derived. The efficiency condition under which the modified estimator is more efficient than existing ones were also presented. Empirical study using four sets of populations was conducted and the results revealed that the proposed estimator was more efficient.
In this study, a new exponential ratio-regression estimator is developed using an auxiliary variable for estimating the finite population mean under a two-phase sampling system. The Bias and Mean Square Error (MSE) of the proposed estimator are derived and compared with some of the estimators in extant literature. Thus, the conditions under which the proposed estimator is better than some existing estimators are provided. Empirically, using four real datasets and simulation study, the proposed estimator performs better than the classical ratio, classical regression, exponential ratio, and exponential regression cum ratio estimator when compared using the criteria of bias, mean square error and percentage relative efficiency. The proposed estimator can be used to estimate the averages of economic variables such as inflation, exchange rate, and standard of living for policy formulation.
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