Spring 2008

Instructor: Antar Bandyopadhyay (Email: antar (at) isid (dot) ac (dot) in Office: 208 Faculty Building).

Class Time: Tu Th 11:30 - 13:00, F 14:00 - 15:00 in Class Room 23.

Instructor's Office Hours: F 15:30 - 17:30 at Room # 208.

Course Duration: January 7 -- April 18, 2008.

Mid-Term Examination Date: February 28, 2008 (Thursday)

Final Examination Date: April 23, 2008 (Wednesday)

Course Outline:

• Linear statistical models/Gauss-Markov Models.
• Least square estimation, Estimable linear functions, Normal equations, Best Linear Unbiased Estimates (BLUEs).
• Gauss-Markov Theorem.
• Variance of BLUEs.
• Normality assumption of error. Maximum likelihood estimation vs Least square estimation/MLE vs BLUE. MVUE vs BLUE.
• Estimation of error variance. Degrees of freedom. Fundamental Theorems of Least Square. Testing of linear hypotheses.
• Various different linear models and ANOVA.
• One way classification.
• Two way classification with and without interactions. Equal and unequal number of observations per cell. Tukey's One Degree of Freedom test.
• Nested classification model.
• Three way classification, various different types of interactions.
• Multiple regression.
• Multiple comparisons.
• Analysis of Covariance (ANCOVA).
• Random Effect Models.
• Basic idea of Log-Linear Models and Logistic regression (will be done by Dr. T. Krishnan).
• Some basics of Generalized Linear Models (GLMs), linear predictor, link function, canonical link function, deviance. Maximum likelihood estimation, iteratively re-weighted least square algorithm. Goodness of fit test. Examples including logit and probit analysis.

Prerequisites:

• Liner Algebra (at the level of Finite Dimensional Vector Spaces, by P. R. Halmos).
• Basic Statistical Inference (at the level of Mathematical statistics by Peter J. Bickel and Kjell A. Doksum).

References:

• Plane Answers to Complex Questions by R. Christensen.
• Linear Statistical Inference by C. R. Rao.
• Linear Models, An Integrated Approach by D. Sengupta and S. R. Jammalamadaka.
• Log-Linear Models by R. Christensen.
• Generalized Linear Models by P. McCullagh and J. A. Nelder.

• Assignments: 15% of the total credit.
• Two Quizes: 10% of the total credit.
• Midterm Exam: 25% of the total credit.
• Final Exam: 50% of the total credit.

Assignment Policies:

• There will be a total of 6 or 7 sets of homework assignments each carrying a total of 20 points.
• The assignments will be given in class every alternate Fridays, starting from the first week of the semester. That is, the first assignment will be given on January 11, 2008, the second assignment will be given on January 25, 2008, and so on.
• An assignment given on a Friday will cover the topics discussed in the lectures in that week and the following week. For example, the first assignment dated January 11, 2008, will cover lecture materials of the first and the second week of the semester.
• You DO NOT need to submit the assignments. They will not be graded. Instead, on every Friday, starting from the second week of the course, we will have tutorials where the students will be asked to present their solution on the board. Grades will be given based on the presentations.
• Note, not every one will be asked to present a solution in every tutorial. The selection will be done randomly and over the whole semester it will cover (almost) uniformly all the students.
• If you are not present in a tutorial and your name came in the selection then you will lose a grade for that. But don't worry you will have enough chance anyway.