Study of some exponential-inverse sine-logarithmic imputation techniques under missing data using simulated data

Non-response in a survey refers to the absence of data from selected participants who fail to provide information for various reasons. Imputation is one of the most effective techniques to address non-response in sample surveys and ensure data completeness.  The most commonly used imputation methods are mean imputation, ratio imputation, and the compromised imputation method.  Mean imputation replaces all missing values with the mean of the responded values, thus reducing the variability in the data set.  To maintain a proportional link between variables, the ratio imputation technique is useful, although it assumes a strong linear relationship between the study and auxiliary variables, which may not always hold.  If violated, this can lead to biased results.  The compromised imputation method combines several techniques but still has limitations and may produce biased outcomes when underlying assumptions are not met.  To address these issues, we propose three Exponential-Inverse Sine-Logarithmic (ESL) imputation techniques along with their corresponding point estimators.  We derive the bias and mean square error (MSE) of the proposed estimators and evaluate their performance both theoretically and numerically in comparison with existing methods.  Additionally, simulated population data sets were generated using statistical software to conduct simulation studies.  Percentage relative efficiencies (PRE) were calculated to compare the performance of all estimators with respect to the mean and ratio methods.  Based on the results, we conclude that the proposed imputation techniques outperform the existing ones.