Statistical Inference

STA 332

This course replaces STA 432 for Fall 2025 and remains cross-listed as Math 343. 
Description: 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. 
Prerequisites: Probability (STA 240L or STA 230 or STA 230S or MATH 231)  AND Multivariable Calculus (MATH 202, 202D, 212A, 212D, 219, or 222).
Not open to students with credit for STA 432, STA 532, or STA 732

** available as of 2025-08-15
Typically Offered
Fall and/or Spring