Logarithmic Imputation Estimators for Domain Mean Estimation under Item Nonresponse

Nonresponse is a persistent problem in survey sampling and can substantially reduce the efficiency of domain-specific estimates, particularly when item-nonresponse occurs within domains. Often, conventional approaches such as re-weighting, weight adjustments, calibration, and imputation often fail when response probabilities depend on the survey variable itself. This study develops alternative ratio-type logarithmic imputation estimators for estimating domain means to address item nonresponse and outlier problems under single-stage simple random sampling (SRS). Three imputation schemes are formulated according to the availability and use of auxiliary information, yielding three new estimators. First-order bias and mean squared error (MSE) expressions are derived using Taylor-series approximation, and theoretical efficiency conditions are established relative to selected existing estimators. An Empirical investigation based on household expenditure and income data from the 2020 Integrated Household Finance and Consumption Survey is conducted using the six geopolitical zones of Nigeria as domains and two item-nonresponse scenarios of approximately 60% and 40%. Across the empirical cases, the proposed estimators generally produced lower MSE and higher percentage relative efficiency than the competing estimators, with scheme 2 providing the strongest performance among the three schemes. The findings indicate that the alternative ratio-type logarithmic imputation estimator can improve the efficiency of domain mean estimation when extreme values and item-nonresponse are present. The study extends existing logarithmic imputation methodology by providing domain-specific estimators under alternative auxiliary-information conditions within a single-stage SRS framework.