On the Unification of Auxiliary Information Estimators in Survey Sampling - Lane Christiansen; Sarjinder Singh; Stephen A. Sedory (Journal of the Indian Society of Agricultural Statistics, 2026)
The use of auxiliary information has led to the development of a large number of estimators for improving the efficiency of population mean estimation in survey sampling. This study establishes a unified theoretical framework by demonstrating that many ratio-type, product-type, exponential, logarithmic, and regression-type estimators proposed in recent decades are special cases of the pioneering general class of estimators introduced by Srivastava (1971) and the wider class proposed by Singh and Upadhyaya (1986). Analytical expressions of mean squared error are presented, and it is shown that the minimum mean squared error achievable under Srivastava’s class is equal to that of the classical linear regression estimator, while the Singh and Upadhyaya class provides a broader framework with additional flexibility. A recently proposed log-ratio estimator is examined and shown to require continuity-based patching. The results confirm the fundamental role of the Srivastava, and Singh and Upadhyaya classes as the underlying unifying structure for auxiliary information estimators and provide practical guidance for selecting efficient estimators in finite and large population settings.