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.

IMPORTANT!

There is a charge for each student. It will be covered by the home university/organisation of the participant.
Prerequisite for the course is a Master's Degree in Statistics, Mathematical Statistics, or related. However, local master students are welcome to follow the presentations.
Those who intend to participate please contact Krzysztof.Podgorski@stat.lu.se. We kindly ask you to consult participation with your main supervisor.
In the email requesting registration to the course, please, include:
- the name and e-mail address of a participant,
- the name and e-mail address of her/his main advisor,
- the name and e-mail address of a person in the home organization to be contacted about the invoice.
Please, send the above information by the 1st of November (but earlier registration will be appreciated and will allow for a better allocation of resources).

Textbook:

The lecture will be entirely based on the following textbook
- Bickel, Peter J.; Doksum, Kjell A. Mathematical statistics‚ basic ideas and selected topics. Vol. 1. Second edition. Texts in Statistical Science Series. CRC Press, Boca Raton, FL, 2015.
but will be selected and structured to meet specific needs of the course in its time schedule and format.

Lecturers:

Per Gösta Andersson , Department of Statistics, Stockholm University, e-mail: per.gosta.andersson@stat.su.se

Krzysztof Podgorski , Department of Statistics, Lund University, e-mail: Krzysztof.Podgorski@stat.lu.se

Detailed schedule

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.