Not all estimators are equal. We evaluate them based on specific mathematical properties: Mathematical Definition On average, the estimate equals the truth. Consistency As sample size grows, the estimate hits the target. Efficiency is minimized The estimate has the smallest possible "scatter". Example Visualization: The Bias-Variance Tradeoff
Mathematical statistics is the bridge between pure mathematics and the messy data of the real world. While an "Applied Statistics" lecture might focus on how to use software to run tests, a Mathematical Statistics lecture focuses on the mathematical statistics lecture
This is the heart of the . It moves in a cycle: Not all estimators are equal
When choosing an estimator, we often look at the , which combines bias and variance. we often look at the