714—Linear Statistical Models. (3) (Prereq: STAT 513 and MATH 544 or STAT 712 or equivalent) A study of the general linear statistical model and the linear hypothesis. Topics include the multivariate normal distribution, distributions of quadratic forms, and parameter estimation and hypothesis testing for full-rank models, regression models, and less than full-rank models.
Sample Course Homepage: Recent Semester
Usually Offered: Fall Semesters
Purpose: To provide a rigorous analytical treatment of the general linear statistical model based on the calculus of linear algebra.
Current Textbook: Rencher, A. C. (2008). Linear Models in Statistics. Hoboken, NJ: John Wiley & Sons.
| Topics Covered |
|
Time |
| Review of matrix algebra. Generalized and conditional inverses; Idempotent matrices and quadratic forms; Matix optimization. |
|
2 weeks |
| Distributions. Random vectors; Multivariate normal distribution; Non-central chi-square and F-distributions; Distribution of quadratic forms. |
|
3 weeks |
| Linear regression models. Estimation and inference for the simple linear model; Non-homogeneous variance; Calibration; Multiple linear regression; Tests of hypotheses; Confidence regions/Confidence intervals; Simultaneous inference; Diagnostics; Partial correlation. |
|
5 weeks |
| The general linear model. ANOVA models; Cell-means models; Fixed and mixed-effects models; Reparameterization; Estimability; Expected mean squares; Contrasts. |
|
4 weeks |
The above textbook and course outline should correspond to the most recent offering of the course by the Statistics Department. Please check the current course homepage or with the instructor for the course regulations, expectations, and operating procedures.
Contact Faculty: Edsel Peña, Joshua Tebbs