Evaluating the Relationship Between Statistical Efficiency and Estimator Bias in Finite Sample Inference

Posted: Feb 01, 2009

• Harper Mitchell
• Liam Moore
• Harper Thomas

Abstract

The conventional paradigm in statistical inference has long emphasized the importance of unbiased estimation, with efficiency considerations typically taking secondary importance. This preference is deeply embedded in statistical pedagogy and practice, with unbiased estimators like the sample mean and ordinary least squares occupying privileged positions in the methodological toolkit. However, this philosophical commitment to unbiasedness often comes at the cost of statistical efficiency, particularly in finite sample settings where the large-sample properties that justify many common procedures may not apply. The tension between these two fundamental properties of estimators—bias and efficiency—represents one of the most enduring and practically significant dilemmas in statistical theory.