Statistical Inference I (7.5 hp) Ph.D. course for students in Statistics, Mathematical Statistics, and related areas - Fall 2020 |
Components: 20 Lectures, 5 Tutorials, 10 Homework Assignments.
Organization: There will five on-line sessions as listed in the schedule below.
Textbook:
The lecture will be entirely based on the following textbook
Lecturers:
Session # and location | Date and time | Topic | Supporting material and comments | Assignment |
---|---|---|---|---|
1 (online - Zoom) | Thursday, November 26, 10:15-11:00 | Introduction -- Data, Models, Parameters, and Statistics | Sections 1.1 and 1.3 of the textbook. Lecture 1 Slides | 1.1.1, 1.1.3, 1.1.4, 1.1.6, 1.1.9, Due on the 10th of January |
Thursday, November 26, 13:15-14:00 | Bayesian set-up | Sections 1.2 and 1.3 of the textbook. Lecture 2 Slides | 1.2.3, 1.2.6, 1.2.11, 1.2.12, 1.2.14, 1.2.15, Due on the 10th of January | |
Thursday, November 26, 15:15-16:00 | Sufficiency and exponential Families | Sections 1.5 and 1.6 of the textbook. Lecture 3 Slides | 1.5.2, 1.5.3, 1.5.7, 1.5.15, 1.5.16, 1.6.2, 1.6.5, Due on the 10th of January | |
2 (online - Zoom) | Wednesday, December 9, 13:15-15:00 | Maximum likelihood estimation | Sections 2.2-4 of the textbook Lecture 4 Slides | 2.2.10, 2.2.11, 2.2.12, 2.2.14, 2.2.15, 2.2.16a, 2.4.1, 2.4.2, 2.4.4, 2.4.5, Due on the 10th of January |
Wednesday, December 9, 15:15-17:00 | Consistency and efficiency | Section 3.4, Section 5.2.2 of the textbook Lecture 5 Slides | 3.4.1, 3.4.5ac, 3.4.10, 3.4.11, 3.4.12 Due on the 31st of January | |
Thursday, December 10, 8:15-10:00 | Testing hypothesis and the Neyman-Pearson lemma | Sections 4.1-2 Lecture 6 Slides | 4.1.1, 4.1.3, 4.1.4, 4.1.5, 4.1.6, 4.2.2, 4.2.3, 4.2.8, 4.2.9 Due on the 31st of January | |
Thursday, December 10, 10:15-12:00 | Uniformly most powerful tests | Section 4.3 of the text Lecture 7 Slides | 4.3.1, 4.3.2, 4.3.4, 4.3.6 Due on the 31st of January | |
Thursday, December 10, 13:15-15:00 | Discussion session | The assigned problems from Chapter 1 and 2 of the textbook. | Focus on: 1.2.12, especially part b and c, 1.2.14, Discussion on minimal sufficiency, focusing on how to prove or disprove the minimal part, using 1.5.15 and 1.5.16 as examples, 1.5.16 part iii), 1.1.3, 1.1.4, 1.1.6 (d), 1.2.3 (b), for the part with given X=k, 2.4.1,2.4.2 | |
Thursday, December 10, 15:15-17:00 | Confidence regions | Section 4.4, Section 4.5 of the text Lecture 8 Slides | 4.4.1, 4.4.5, 4.4.6, 4.4.10, 4.4.14, 4.5.1, 4.5.2, 4.5.12 Due on the 31st of January | |
Friday, December 11, 8:15-10:00 | Frequentist and Bayesian formulations | Section 4.7, Section 1.2, Section 1.6.3 of the text] Lecture 9 Slides | 4.7.1, 4.7.2, 4.7.3, 4.7.4ab Due on the 31st of January | |
Friday, December 11, 10:15-12:00 | Prediction intervals | Section 4.8 of the text Lecture 10 Slides | 4.8.1, 4.8.2, 4.8.3 Due on the 31th of January | |
Friday, December 11, 12:15-15:00 | Common lunch, round table discussion, conclusions | TBA | TBA | |
3 (online) | Thursday, January 14, 10:15-11:00, Zoom Location | Discussion session | Focus on the problems that are due on the 31st of January | Some specific problems for the discussion: 4.1.4, 4.2.2 b), 4.2.3 c), 4.5.12, 4.4.14 d), 4.7.2 Some initial notes and tips |
Thursday, January 14, 13:15-14:00 | Likelihood ratio procedures | TBA | TBA | |
Thursday, January 14, 15:15-16:00 | Asymptotical Consistency | TBA | TBA | |
4 (online) | Wednesday, January 27, 13:15-15:00 | The Delta Method with Applications | TBA | TBA |
Wednesday, January 27, 15:15-17:00 | Discussion session | TBA | TBA | |
Thursday, January 28, 8:15-10:00 | Asymptotic Theory in One Dimension | TBA | TBA | |
Thursday, January 28, 10:15-12:00 | Inference for Gaussian Linear Models | TBA | TBA | |
Thursday, January 28, 13:15-15:00 | Discussion Session | TBA | TBA | |
5 (online) | Thursday, February 18, 10:15-11:00 | Large Sample Tests and Confidence Regions | TBA | TBA |
Thursday, February 18, 13:15-14:00 | Discussion session | TBA | TBA | |
Thursday, February 18, 15:15-16:00 | Generalized Linear Models | TBA | TBA |
Homeworks will serve as a training for the final examination and covering portions of the material as indicated in the above schedule.
They can contribute maximum 40% of the total score for the course.
Final Take-home Exam will serve as the main assessment of acquired knowledge during the course. The solutions will yield maximum 60% of the total score. After returning the take-home exam there will be scheduled a 15 min conversation with each participant of the course about the solutions to the exam and homework problems. After this the final grade will be assigned. It will be a passing grade if at least 55% of the total score is collected.