---

title: Statistic Estimation

date: '2026-07-20 18:18:00'

tags:

- Statistics

cover: https://img.yulecna.top/posts/yn-background.jpg

description: ''

---
1. **Loss Function**: Measures how bad it is to guess $g(\theta)=d$. Defined as 
   $$
   L(g(\theta), d)
   $$
2. **Risk**: Measures the average performance over the whole range of dataset X that we might observe, defined as
   $$
   R(\theta, \delta(\cdot)) = \mathbb{E}_\theta[L(\theta, \delta(X))] = \int L(\theta, \delta(x))d P_\theta(x)
   $$
	1. Average-case risk
	2. worst-case risk
3. **Unbiased Estimator**