Optimality in Decision Theory: Unbiased Estimation

This lecture covers the optimality in the decision theory framework, focusing on unbiased quadratic estimation. It discusses the sufficiency and 'Rao-Blackwellization', completeness in uniform optimality, and lower bounds for the risk. The role of unbiasedness and sufficiency in estimation is explored, along with examples illustrating the challenges and limitations of unbiased estimators. The lecture also delves into the asymptotic properties of the maximum likelihood estimators and the Cramér-Rao lower bound. Various theorems and conditions are presented to understand the optimality of estimators and the importance of sufficient statistics in achieving unbiased estimations.