Optimal Estimation and Bias in Statistics

This lecture discusses the concept of optimal estimation and the role of bias in finite samples. It explores how likelihood estimators are essentially optimal asymptotically, cautioning about their interpretation for finite sample sizes. The delicate tradeoff between bias and variance is crucial in both parametric and nonparametric estimation, illustrated with examples like the James-Stein Estimator. The lecture also covers the impact of bias on reducing variance in finite samples and the importance of understanding this tradeoff in statistical estimation.