Advanced statistical inference
Graduate · Statistics
Syllabus focus
Theoretical / proof-based
Pricing
Graduate-level rates are set on consultation. See the pricing page for K–12 and undergraduate rates.
Topics typically covered
Theoretical / proof-based
Estimation theory
- Minimax and Bayes estimation
- Asymptotic efficiency and LAN
- Edgeworth and bootstrap refinements (intro)
- Empirical process introduction
- Nonparametric density estimation theory (overview)
Testing and confidence sets
- Likelihood ratio tests: Wilks' theorem proof sketch
- Score and Wald tests
- Multiple testing: FDR and FWER
- Nonparametric testing theory
- Invariance and similarity in testing
Advanced topics
- Semiparametric models (introduction)
- Missing data: MAR and ignorability
- Causal inference connections to potential outcomes
- High-dimensional consistency (preview)
Notes
Second-semester theory course following mathematical statistics. Depth varies by program but typically includes full asymptotic treatment of MLE and LRT.