STA 131C Introduction to Mathematical Statistics
Lecture: 3 hours
Discussion: 1 hour
Testing theory, tools and applications from probability theory, Linear model theory, ANOVA, goodness-of-fit.
Prerequisite: STA 131B; or Consent of Instructor.
Summary of course contents:
- More testing theory (8 lect): LR-test, UMP tests (monotone LR); t-test (one and two sample), F-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 (3 lect) (a) chi^2 test (b) Kolmogorov-Smirnov test (c) Wilcoxon test
Probability and Statistics by Mark J. Schervish, Morris H. DeGroot 4th Edition 2014, Pearson