Mathematical statistics
Graduate · Math
Syllabus focus
Topics typically covered
Click a topic for the full text and related unit practice.
Graduate Mathematical statistics — outline derived from course README sections and typical US statistics syllabi (OpenIntro / standard OER where applicable).
Probability foundations
- Probability spaces and sigma-algebras — Probability spaces and sigma-algebras
- Measures — Measures
- Random variables — Random variables
- Induced measures — Induced measures
- Expectation via Lebesgue integral — Expectation via Lebesgue integral
- Independence and product measures — Independence and product measures
- Convergence modes: a.s., in probability, Lp, in distribution — Convergence modes: a.s., in probability, Lp, in distribution
Distribution and limit theory
- Characteristic functions — Characteristic functions
- Law of large numbers — Law of large numbers
- Central limit theorems — Central limit theorems
- Multivariate normal — Multivariate normal
- Quadratic forms — Quadratic forms
- Sufficient and complete statistics — Sufficient and complete statistics
- Ancillary statistics — Ancillary statistics
- Exponential families — Exponential families
Statistical inference theory
- Point estimation: UMVU and MLE — Point estimation: UMVU and MLE
- Efficiency — Efficiency
- Hypothesis testing: Neyman–Pearson — Hypothesis testing: Neyman–Pearson
- UMP tests — UMP tests
- Confidence sets — Confidence sets
- Duality with testing — Duality with testing
- Asymptotic theory: delta method — Asymptotic theory: delta method
- Fisher information — Fisher information
- Decision theory — Decision theory
- Admissibility (introduction) — Admissibility (introduction)
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Probability foundations
Probability spaces and sigma-algebras
Coming soon - Distribution and limit theory
Characteristic functions
Coming soon - Statistical inference theory
Point estimation: UMVU and MLE
Coming soon
Notes
Graduate Mathematical statistics — outline derived from course README sections and typical US statistics syllabi (OpenIntro / standard OER where applicable). Topic outline: `content/topics/graduate/math_stats.json`.