Modern techniques in variance estimation with auxiliary information: a logarithmic perspective

Abstract

Variance estimation is essential to statistical analysis because it sheds light on the accuracy and dependability of estimations. The effectiveness of traditional methods is frequently increased by using linear connections between the study and auxiliary variables. Nonetheless, the connection between the research variable and auxiliary data may exhibit a nonlinear pattern, namely a logarithmic shape, in several real-world scenarios. A family of variance estimators that use logarithmic connections with auxiliary variables to increase accuracy is proposed in this study in recognition of this. Real-world situations where data show multiplicative impacts or exponential development patterns, where logarithmic modeling is more suitable than linear assumptions, are the driving force behind this approach. The usefulness of the suggested estimators is illustrated by real-world examples, including biological measures, income distribution studies, and environmental data assessments. To evaluate the performance in general, theoretical characteristics are derived, such as mean square error and bias. The superiority of the logarithmic approach over traditional techniques is further supported by numerical examples and simulations, which offer a reliable and adaptable tool for variance estimates in a variety of domains. © 2025 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the University of Bahrain.