# STA 200C Introduction to Mathematical Statistics II

Units: 4

Format:
Lecture: 3 hours
Discussion: 1 hour

Catalog Description:
Testing theory, tools and applications from probability theory, Linear model theory, ANOVA, goodness-of-fit.

Prerequisite: STA 200B; or Consent of Instructor.

Summary of course contents:

• Concepts of testing hypothesis (6 lect): LR-­-test, UMP tests (monotone LR); t-­-test (one and two sample), F-­-test; one-­-sided t-­-test as LR-­-test; duality of confidence intervals and testing
• Tools from probability theory (2 lect) (including Cebychev's ineq., LLN, CLT, delta-­-method, continuous mapping theorems)
• Applications of (II) (6 lect): (i) consistency of estimators; (ii) variance stabilizing transformations; (iii) asymptotic normality (and efficiency) of MLE; (iv) large sample tests; (v) large sample confidence intervals
• Linear model theory (10-­-12 lect) (a) LS-­-estimation (b) Simple linear regression (normal model): (i) MLEs / LSEs: unbiasedness; joint distribution of MLE's; (ii) prediction; (iii) confidence intervals (iv) testing hypothesis about regression coefficients (c) General (normal) linear model (MLEs; hypothesis testing (d) ANOVA
• Goodness-­-of-­-fit (4 lect) (a) chi^2 test (b) Kolmogorov-­-Smirnov test (c) Wilcoxon test Suggested material to be covered via reading assignments: -­- Bayes tests -­- Additional tools for large sample inference: general delta-­-method (non-­-normal limit; second order version) -­- Other non-­-parametric methods, such as kernel estimation, permutation test, two-­-sample rank tests

Restrictions:
No credit to students who have taken course 131C.