Entropy-Based Adaptive Ratio Estimators in Stratified Sampling Using Information Theory Measures with Empirical and Simulation Evidence

In this work, it is proposed to make use of information-theoretic measures including Shannon and Rényi entropy to estimate the population means in stratified sampling by introducing a new Entropy-Based Adaptive Ratio Estimator (EBARE) framework. In contrast to the old ratio estimators, which presuppose constant strata weights, the given method dynamically adjusts to the informational contribution of each stratum to reduce the estimation bias and the mean square error with the help of the entropy weighted allocation. Entropy integration measures the uncertainty and gain in information of auxiliary variables to allow efficient utilization of heterogeneous data structures. Analytical derivation of the theoretical properties of the proposed estimator such as bias, efficiency and asymptotic variance are done and compared to the classical and exponential ratio estimators. An extensive Monte Carlo study has shown that EBARE is always better than current estimators in both normal and uncommon correlation and variability conditions and provides an informative, adaptable augmentation to current sampling models, particularly in the scenarios of big data and multi-source survey designs.