Log-transformed approaches to variance estimation using auxiliary data

Abstract

Reliable statistical inference requires accurate population variance estimate, especially in domains where measurement limitations and intrinsic variability impact data. Applying traditional estimators to skewed or heavy-tailed populations frequently results in inefficient results. We provide a novel class of generalized logarithmic variance estimators that use logarithmic transformations and auxiliary data to stabilize variance and improve estimator performance in order to overcome this constraint. We calculate the suggested estimators’ bias and Mean Squared Error (MSE) expressions and assess their effectiveness using comprehensive Monte Carlo simulations with different sample sizes. The suggested estimator, $T_{r1-}$, produces a significant reduction in MSE up to 57% increase in efficiency (PRE) at n=600 when compared to the usual estimator. The suggested methodologies resilience and suitability for high-variability situations are further confirmed using real-world datasets. In every context, the findings show that the suggested estimators perform better than the current ones in terms of lower MSE and greater PRE. This research demonstrates how logarithmic transformations may be used to create variance estimators that are more accurate and effective, especially when auxiliary variables are provided.