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.

Illustrative reading:
M.H. DeGroot and M.J. Shervish: Probability and Statistics, Addison Wesley

G.G. Roussas: An introduction to Probability Theory and Statistical Inference, Elsevier  

GE3:
SE

Potential Overlap:
The course material for STA 200C is the same as for STA 131C with the exception that students in STA 200C are given additional advanced reading material and additional homework assignments. The midterm and final examinations will differ from those of 131C in that they will include material covered in the additional reading assignments.

History:
First offered Spring 2017.