Improved classes of logarithmic type estimators of finite population mean in case of missing data

The situation of missing observations is a common issue in surveys and other data collection processes. This issue can seriously affect the statistical inference. The imputation techniques are widely recognized as an effective means of addressing this challenge. Over the years, several estimators or classes of estimators have been proposed to reduce the bias and mean square error of various existing estimators of interest in the presence of missing data, particularly by utilizing auxiliary information. In this paper, we have proposed some new classes of logarithmic type estimators of the population mean when missing values are there in the sample data. We derive the approximate expressions for the bias and mean square errors of these classes. The optimum mean square errors of these proposed estimators are compared with those of the existing estimators. A numerical investigation is used to validate the conclusions so acquired. This investigation illustrate that the proposed estimators outperform their present counterparts across all the situations under consideration, as evidenced by consistently higher percent relative efficiencies.