Statistical Inference I (7.5 hp)

Ph.D. course for students in Statistics, Mathematical Statistics, and related areas - Spring 2025

Components: 20 Lectures, 5 Tutorials, 10 Homework Assignments

Organization: There will be five sessions as listed in the schedule below.

Krzysztof Podgórski , Department of Statistics, Lund University, e-mail: Krzysztof.Podgorski@stat.lu.se is responsible for the first three sessions and the material associated with them.
Per Gösta Andersson , Department of Statistics, Stockholm University, e-mail: per.gosta.andersson@stat.su.se is responsible for the remaining two sessions and the material associated with them.
The first three sessions will be hybrid: in-class in Lund and online through Zoom. The lectures of the first three sessions will be recorded and the recording will be made available after the sessions.
Students outside of Lund are very much welcome to come to Lund to participate. In particular, Session 2, Nov. 16-17 is planned to accommodate both research and social interaction. The cost of travel and accommodation is on your home institution.
The entirely distant participation is also possible.
The schedule of the remaining two sessions at Stockholm is approximate and information on their timetable and organization will be given by Per Gösta Andersson.

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. Having also the second volume of this textbook can be beneficial for further studies of the principles of modern statistics but is not necessary for understanding the material of this course.

Detailed schedule

Session # and location	Date and time	Topic	Supporting material and comments	Assignment
1 xxx online - Zoom	xxx	Introduction -- Data, models, parameters, and statistics, Bayesian set-up.	Sections 1.1, 1.2, and 1.3 of the textbook. Lecture 1 Slides and Lecture 2 Slides	1.1.1, 1.1.3, 1.1.4, 1.1.6, 1.1.9, 1.2.3, 1.2.6, 1.2.11, 1.2.12, 1.2.14, 1.2.15,
1 xxx online - Zoom	xxx	Sufficiency and exponential Families, Maximum likelihood estimation	Sections 1.5 and 1.6 of the textbook, Sections 2.2-4 of the textbook Lecture 3 Slides and Lecture 4 Slides	1.5.2, 1.5.3, 1.5.7, 1.5.15, 1.5.16, 1.6.2, 1.6.5, 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,
xxx online - Zoom	xxx	General theory of estimation.	Section 3.4 of the textbook Lecture 5 Slides	3.4.1, 3.4.5ac, 3.4.10, 3.4.11, 3.4.12,
	xxx	Consistency and efficiency.	Section 5.2.2,
	xxx	Testing hypothesis and the Neyman-Pearson lemma	Section 4.1-2 of the text 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,
	xxx	Uniformly most powerful tests, Confidence regions.	Sections 4.3-5 of the text Lecture 7 Slides and Lecture 8 Slides	4.3.1, 4.3.2, 4.3.4, 4.3.6, 4.4.1, 4.4.5, 4.4.6, 4.4.10, 4.4.14, 4.5.1, 4.5.2, 4.5.12,
	xxx	Common lunch, round table discussion, conclusions	The assigned problems from Chapter 1 and 2 of the textbook.	The assigned problems from Chapter 1 and 2 of the textbook.
3 xxx online - Zoom	xxx	Frequentist and Bayesian formulations, Prediction intervals	Section 4.7, Section 1.2, Section 1.6.3, Section 4.8 of the text Lecture 9 Slides and Lecture 10 Slides	4.7.1, 4.7.2, 4.7.3, 4.7.4ab,4.8.1, 4.8.2, 4.8.3
3 xxx online - Zoom	xxx	Likelihood ratio procedures, Asymptotical Consistency, Discussion	Section 4.9.1-4 Section 5.2.1 Lecture 11 Slides	Some comments and tips
4	TBA	The Delta Method with Applications	TBA	TBA
	TBA	Asymptotic Theory in One Dimension	TBA	TBA
	TBA	Inference for Gaussian Linear Models	TBA	TBA
5	TBA	Large Sample Tests and Confidence Regions	TBA	TBA
5	TBA	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. Each assignment is made of the list of problems. There is also a link to some solutions (not necessary perfect). The homework assignment requires: 1) Grading all provided solution for each problem on the scale from 1 to 10; 2) Choosing three problems from the list that did not receive grade 10 and providing a solution that aims at improving the score. If there are enough problems on the list to improve (graded below 10), then find problems from the text from the same section but that are not on the list and provide solutions to these problems. After the submission of the grading they will be summarized in a table with averaged grades, and your solutions will be graded by your peers and added to the list of grades.

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. The final exam will be chosen from the problems on the list and selected individually based on the obtained submission of assignment in a way that will seek an improvement of both the grades and the solutions.