Statistics Asymptotic Theory
- 1 min All opinions are my own.These notes are from STAT 553 Asymptotic Theory by Professor Jogesh Babu, written with detailed proofs and examples in asymptotic statistics.
Probability, Borel-Cantelli Lemma, Probability Inequalities, Convergence, Dominated Convergence Theorem
Law of Large Numbers, Characteristic Functions
Continuity Theorem, Tightness
Central Limit Theorem
Delta Method, Variance Stabilizing Transformation
Cramer-Wold Theorem, Multivariate CLT
Smooth Function Model CLT, Order Statistics Limiting Distribution
Sample Quantiles, Bahadur’s Representation
Consistency of MLE, Cramer’s Theorem
Cramer-Rao’s Lower Bound, Asymptotic Efficiency, Likelihood Based Test Statistics
Jackknife’s Consistency, Bootstrap Method
U Statistics, V Statistics
Ying Zhang
Ride with Uncertainties.