MATH 343 · also STA 332
Statistical Inference
Sifan Liu
Description from DukeHub
Definition of a random sample, statistical model, and likelihood. Definition and properties of estimators and sufficient, ancillary, and complete statistics. Point estimation: comparing estimators in a decision-theoretic framework (loss functions, risk, mean squared error) and optimality results (Uniform Minimum Variance Estimators, Fisher's information, Cramér-Rao bound). Hypothesis testing: comparing testing procedures and constructing optimal tests within the Neyman-Pearson framework. Tests based on the likelihood ratio. Confidence intervals: construction based on inverting tests. Asymptotic considerations: consistent and asymptotically efficient estimators. Likelihood-based asymptotic tests and confidence intervals.
Skills
- data and statisticsdescription: "statistical" and 2 more
AI-resilient: 1 of 5
- No: Physical, lab or field work
- No: Live work with people
- Yes: Judgment someone is accountable for · "decision"
- No: A craft you practice with your hands or body
- No: Small, in-person format
The checks lean on Microsoft Research, Working with AI (2025), which found generative AI applies least to physical work and hands-on work with people. A signal, not a promise. How the score works
More in MATH
- Laboratory Calculus and Functions I MATH 105L
- Laboratory Calculus and Functions II MATH 106L
- Laboratory Calculus I MATH 111L
- Laboratory Calculus II MATH 112L
- Elements of Mathematical Modeling MATH 160CN
- Multivariable Calculus for Economics MATH 202D