On the development of survey methods for novel mean imputation and its application to abalone data

Non-response in surveys is a common problem faced by surveyors, this results in missing data. Missing values are often omitted when doing any statistical analysis, but this reduces the sample size and consequently decreases the precision of estimates. In such situations, imputation is a commonly used method to deal with missing data, this involves estimating the missing values based on the observed data. In this paper, we propose two new estimators for the finite population mean, formulated using two suggested sampling methods and their associated imputation strategies. We derive the variance of the proposed estimators and obtain conditions under which these estimators are more efficient than existing estimators. We conduct a simulation study to assess the relative efficiency (RE) of the proposed estimators for varying sample sizes, response rates, and ranking criteria. For real-world application, we consider data on measuring the characteristics of abalone. The simulation results demonstrate that the proposed mean estimators based on the suggested imputation methods are more efficient than the existing methods in estimating the mean of the finite population.