Prerequisites for Maximum Likelihood Estimation: Theory, Information Identity, and Asymptotic Efficiency

Direct prerequisites (8)

1. Common Probability Distributionslayer 0A, tier 1
2. Differentiation in Rⁿlayer 0A, tier 1
3. Central Limit Theoremlayer 0B, tier 1
4. KL Divergencelayer 1, tier 1
5. Exponential Function Propertieslayer 0A, tier 1
6. Information Theory Foundationslayer 0B, tier 2
7. Method of Momentslayer 0B, tier 2
8. Radon-Nikodym and Conditional Expectationlayer 0B, tier 1

Reachable through the chain (22)

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.

• Sets, Functions, and Relationslayer 0A, tier 1
• Basic Logic and Proof Techniqueslayer 0A, tier 2
• Integration and Change of Variableslayer 0A, tier 2
• Measure-Theoretic Probabilitylayer 0B, tier 1
• Cardinality and Countabilitylayer 0A, tier 2
• Kolmogorov Probability Axiomslayer 0A, tier 1
• Random Variableslayer 0A, tier 1
• Zermelo-Fraenkel Set Theorylayer 0A, tier 2
• Vectors, Matrices, and Linear Mapslayer 0A, tier 1
• Continuity in Rⁿlayer 0A, tier 1
• Metric Spaces, Convergence, and Completenesslayer 0A, tier 1
• Law of Large Numberslayer 0B, tier 1
• Expectation, Variance, Covariance, and Momentslayer 0A, tier 1
• Joint, Marginal, and Conditional Distributionslayer 0A, tier 1
• Triangular Distributionlayer 0A, tier 2
• Borel-Cantelli Lemmaslayer 0B, tier 1
• Modes of Convergence of Random Variableslayer 0B, tier 1
• Characteristic Functionslayer 1, tier 1
• Moment Generating Functionslayer 0A, tier 2
• Distance Metrics Comparedlayer 1, tier 2
• Non-Euclidean and Hyperbolic Geometrylayer 1, tier 2
• Total Variation Distancelayer 1, tier 1