Theoretical / proof-based
Advanced statistical inference · Graduate · Math
Learning objectives from the Advanced statistical inference syllabus, grouped by unit. Click an objective for study materials.
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)
Learning objectives
Click an objective for study materials.
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)
Definitions and structure
- 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
Proofs and reasoning
- Nonparametric density estimation theory (overview) — Nonparametric density estimation theory (overview)
- 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
Abstraction and generalization
- Invariance — Invariance
- Similarity in testing — Similarity in testing
- 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
Modeling and computation
- Apply minimax and bayes estimation in engineering contexts — Apply minimax and bayes estimation in engineering contexts
- Apply asymptotic efficiency and lan in engineering contexts — Apply asymptotic efficiency and lan in engineering contexts
- Apply edgeworth in engineering contexts — Apply edgeworth in engineering contexts
- Apply bootstrap refinements (intro) in engineering contexts — Apply bootstrap refinements (intro) in engineering contexts
- Apply empirical process introduction in engineering contexts — Apply empirical process introduction in engineering contexts
Data and technology
- Use software to explore advanced statistical inference problems numer... — Use software to explore advanced statistical inference problems numerically
- Interpret computational results against analytic predictions — Interpret computational results against analytic predictions
- Build spreadsheets or scripts for routine calculations — Build spreadsheets or scripts for routine calculations
- Visualize functions, fields, or datasets tied to course topics — Visualize functions, fields, or datasets tied to course topics
- Connect course methods to lab, industry, or research workflows — Connect course methods to lab, industry, or research workflows
Problem-solving practice
- Nonparametric density estimation theory (overview) — Nonparametric density estimation theory (overview)
- 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
Multi-Unit Problems
Course-level sets that combine skills across study units (coming soon).
Browse Multi-Unit ProblemsWhat each unit includes
Open a unit below for full materials. Typical resources:
- Study guide
- Exam Strategy
- Common Mistakes
- Worksheets
- Word problems
- Mixed Practice
- Multi-Unit Problems
- Review
- Practice test
- Answer key
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
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$1,162 · Advanced statistical inference · 18 tutoring hrs
Study guides, worksheets, reviews, practice tests, and answer keys for 1 class. 18 tutoring hours (1 hr / week · semester). Bundle discount applied vs buying separately. Pay in full via Zelle.