The course will present the core introductory materials of large sample theory for statistical estimation and testing. The students are expected to have already taken basic probability theory and mathematical statistics.
The course will cover the following topics:
1. Review of probability theory (notions of convergences, LLN, CLT, etc).
2. Asymptotic distributions of sample quantiles, order statistics, and extremes.
3. Efficient estimation and testing theory (consistency, convergences of MLE, asymptotic efficiency and normality, asymptotic normality of posteriors, relative efficiency, asymptotic distributions of LRT statistics, asymptotic distribution of chi-square tests).
4. Additional topics (time permitting): M-estimation, bootstrap, VC-theory.
