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Statistic Estimation

2026-07-20 18:18:00# Statistics
  1. Loss Function: Measures how bad it is to guess g(θ)=dg(\theta)=d. Defined as L(g(θ),d)L(g(\theta), d)
  2. Risk: Measures the average performance over the whole range of dataset X that we might observe, defined as R(θ,δ(⋅))=Eθ[L(θ,δ(X))]=∫L(θ,δ(x))dPθ(x)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