Asian Journal of Probability and Statistics

In this paper, we intend to proposed modified regression-cum-exponential type mean imputation schemes under two-stage cluster sampling. We came up with the proposed strategy after having identified the gaps in the previous study, that is the responses of the respondents in the previous research imputation schemes were not directly used as they were computed using some exponential functions, this approach leads to manipulation of opinions of respondents as their actual responses were not directly utilized which may affect the efficiency of the estimator of the schemes. Also, exponential ratio-type estimator which requires strong and positive correlation between the study and auxiliary variables, was utilized to estimate the responses of non-respondents information. Therefore, if the correlation between the study and auxiliary variables is less than 0.5 (fair or poor correlations) or negative, the efficiency of the estimate drastically reduces leading to either over-estimation or under-estimation, as a result of these gaps prompted us into the current research.The properties (Biases and MSEs) of the proposed estimators were derived up to first order approximation using Taylor’s series approach. The empirical studies were conducted using simulated data sets to investigate the efficiency of the proposed estimators over the efficiency of the existing estimators. The results revealed that the proposed estimators have higher percentage relative efficiencies (PREs). This implies that the proposed estimators are more efficient and can produce better estimate of the population mean compared to other existing estimators considered in this study.The importance of this study is to obtain new and efficient estimators of population mean in two-stage cluster sampling. These new estimators can be used to produce highly efficient estimate of population mean of any study variable in any field of endeavor.