Statistics Asymptotic Theory

- 1 min

These notes are from STAT 553 Asymptotic Theory by Professor Jogesh Babu in a written format with details of proofs and examples in statistics asymptotic theory.

Probability, Borel-Cantelli Lemma, Probability Inequalities, Convergence, Dominated Covergence Theorem

Note 1

Law of Large Numbers, Characteristics Functions

Note 2

Continuity Theorem, Tightness

Note 3

Central Limit Theorem

Note 4

Delta Method, Variance Stabilizing Transformation

Note 5

Cramer-Wold Theorem, Multivariate CLT

Note 6

Smooth Function Model CLT, Order Statistics Limiting Distribution

Note 7

Sample Quantiles, Bahadur’s Representation

Note 8

Consistency of MLE, Cramer’s Theorem

Note 9

Cramer-Rao’s Lower Bound, Asymptotic Efficiency, Likelihood Based Test Statistics

Note 10

Jackknife’s Consistency, Bootstrap Method

Note 11

U Statistics, V Statistics

Note 12

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