Prerequisites for Shrinkage Estimation and the James-Stein Estimator: Inadmissibility, SURE, and Brown's Characterization

Direct prerequisites (3)

1. Maximum Likelihood Estimation: Theory, Information Identity, and Asymptotic Efficiencylayer 0B, tier 1
2. Cramér-Rao Bound: Information Inequality, Achievability, and Sharper Variantslayer 0B, tier 1
3. Minimax Lower Bounds: Le Cam, Fano, Assouad, and the Reduction to Testinglayer 3, tier 1

Reachable through the chain (16)

These topics are not directly cited as prerequisites but are reached transitively by following the chain upward. Working through the direct prerequisites pulls these in.

• Common Probability Distributionslayer 0A, tier 1
• Sets, Functions, and Relationslayer 0A, tier 1
• Basic Logic and Proof Techniqueslayer 0A, tier 2
• Differentiation in Rnlayer 0A, tier 1
• Vectors, Matrices, and Linear Mapslayer 0A, tier 1
• Continuity in Rⁿlayer 0A, tier 1
• Metric Spaces, Convergence, and Completenesslayer 0A, tier 1
• Central Limit Theoremlayer 0B, tier 1
• Law of Large Numberslayer 0B, tier 1
• Random Variableslayer 0A, tier 1
• Kolmogorov Probability Axiomslayer 0A, tier 1
• Expectation, Variance, Covariance, and Momentslayer 0A, tier 1
• KL Divergencelayer 1, tier 1
• Information Theory Foundationslayer 0B, tier 2
• Fisher Information: Curvature, KL Geometry, and the Natural Gradientlayer 0B, tier 1
• Concentration Inequalitieslayer 1, tier 1