Sampling Estimators and Properties of a Good Estimator: A Theoretical and Applied Perspective

Estimators are essential tools in survey sampling, enabling the approximation of unknown population parameters from limited sample data. Full population surveys are often impractical due to cost, time, and logistical constraints, making estimators such as the sample mean, ratio, regression, and stratified estimators indispensable. This paper reviews the theoretical foundations of these estimators, emphasizing their key properties—unbiasedness, consistency, efficiency, sufficiency, and minimum mean square error (MMSE). Analytical expressions for bias and mean square error health, and social sciences are discussed, along with modern developments such as bootstrap and jackknife resampling, Bayesian estimation, and approaches for big data and adaptive sampling. The paper highlights the balance between unbiasedness and efficiency, illustrating how classical and contemporary estimators remain central to reliable statistical inference in increasingly complex survey contexts.