PhD Course in REGRESSION AND VARIANCE ANALYSIS

Course Description:

1. Statistical concepts such as sufficiency and completeness
2. Subspaces and projections
3. Discussion of different criterias for estimation such as unbiasedness, invariance and linearity
4. Invariance estimation, Gauss-Markov theorem on linear estimators (BLUE)
5. Testing hypothesis in linear models
6. Basic F-test as projection
7. Power of F-test. Non-central F- and t-distribution
8. Theory of matrix algebra and its relation to projections
9. Some typical variance analysis problem
10. The optimality and invariance of variance analysis
11. Estimation with extra conditions. Admissible estimators. Robustness.
12. Linear models with random effects
13. Generalized inverses for linear models

Literature:
Arnold, Steven F. (1981), The theory of linear models and multivariate analysis, John Wiley & Sons, Inc.

The course will cover Chapters 1-7 and Sections 15.1-15.3 of the above book. If required, some theory of matrix algebra will be covered in more depth than the Appendix in the book.