Prerequisite chain
Prerequisites for Asymptotic Statistics: M-Estimators, Delta Method, LAN
Topics you need before working through Asymptotic Statistics: M-Estimators, Delta Method, LAN. Direct prerequisites are listed first; transitive prerequisites (the chain reachable through them) follow.
Direct prerequisites (6)
- Central Limit Theoremlayer 0B, tier 1
- Maximum Likelihood Estimation: Theory, Information Identity, and Asymptotic Efficiencylayer 0B, tier 1
- Modes of Convergence of Random Variableslayer 0B, tier 1
- Cramér-Rao Bound: Information Inequality, Achievability, and Sharper Variantslayer 0B, tier 1
- Cramér-Wold Theoremlayer 1, tier 2
- Fisher Information: Curvature, KL Geometry, and the Natural Gradientlayer 0B, tier 1
Reachable through the chain (36)
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.
- Law of Large Numberslayer 0B, tier 1
- Random Variableslayer 0A, tier 1
- Kolmogorov Probability Axiomslayer 0A, tier 1
- Sets, Functions, and Relationslayer 0A, tier 1
- Basic Logic and Proof Techniqueslayer 0A, tier 2
- Expectation, Variance, Covariance, and Momentslayer 0A, tier 1
- Common Probability Distributionslayer 0A, tier 1
- Exponential Function Propertieslayer 0A, tier 1
- Integration and Change of Variableslayer 0A, tier 2
- Measure-Theoretic Probabilitylayer 0B, tier 1
- Cardinality and Countabilitylayer 0A, tier 2
- Zermelo-Fraenkel Set Theorylayer 0A, tier 2
- Joint, Marginal, and Conditional Distributionslayer 0A, tier 1
- Triangular Distributionlayer 0A, tier 2
- Borel-Cantelli Lemmaslayer 0B, tier 1
- Metric Spaces, Convergence, and Completenesslayer 0A, tier 1
- Characteristic Functionslayer 1, tier 1
- Moment Generating Functionslayer 0A, tier 2
- Differentiation in Rⁿlayer 0A, tier 1
- Vectors, Matrices, and Linear Mapslayer 0A, tier 1
- Continuity in Rⁿlayer 0A, tier 1
- KL Divergencelayer 1, tier 1
- Information Theory Foundationslayer 0B, tier 2
- Distance Metrics Comparedlayer 1, tier 2
- Non-Euclidean and Hyperbolic Geometrylayer 1, tier 2
- Total Variation Distancelayer 1, tier 1
- Method of Momentslayer 0B, tier 2
- Radon-Nikodym and Conditional Expectationlayer 0B, tier 1
- Basu's Theoremlayer 0B, tier 3
- Sufficient Statistics and Exponential Familieslayer 0B, tier 2
- Positive Semidefinite Matriceslayer 0A, tier 1
- Eigenvalues and Eigenvectorslayer 0A, tier 1
- Matrix Operations and Propertieslayer 0A, tier 1
- Linear Independencelayer 0A, tier 1
- Inner Product Spaces and Orthogonalitylayer 0A, tier 1
- Matrix Normslayer 0A, tier 1