Advanced statistical inference
Graduate · Math
Syllabus focus
Topics typically covered
Click a topic for the full text and related unit practice.
Graduate Advanced statistical inference — outline derived from course README sections and typical US statistics syllabi (OpenIntro / standard OER where applicable).
Estimation theory
- Minimax and Bayes estimation — Minimax and Bayes estimation
- Asymptotic efficiency and LAN — Asymptotic efficiency and LAN
- Edgeworth — Edgeworth
- Bootstrap refinements (intro) — Bootstrap refinements (intro)
- Empirical process introduction — Empirical process introduction
- Nonparametric density estimation theory (overview) — Nonparametric density estimation theory (overview)
Testing and confidence sets
- Likelihood ratio tests: Wilks' theorem proof sketch — Likelihood ratio tests: Wilks' theorem proof sketch
- Score and Wald tests — Score and Wald tests
- Multiple testing: FDR and FWER — Multiple testing: FDR and FWER
- Nonparametric testing theory — Nonparametric testing theory
- Invariance — Invariance
- Similarity in testing — Similarity in testing
Advanced topics
- Semiparametric models (introduction) — Semiparametric models (introduction)
- Missing data: MAR and ignorability — Missing data: MAR and ignorability
- Causal inference connections to potential outcomes — Causal inference connections to potential outcomes
- High-dimensional consistency (preview) — High-dimensional consistency (preview)
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Estimation theory
Minimax and Bayes estimation
Coming soon - Testing and confidence sets
Likelihood ratio tests: Wilks' theorem proof sketch
Coming soon - Advanced topics
Semiparametric models (introduction)
Coming soon
Notes
Graduate Advanced statistical inference — outline derived from course README sections and typical US statistics syllabi (OpenIntro / standard OER where applicable). Topic outline: `content/topics/graduate/advanced_inference.json`.