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. We plan 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: All problems from slides and
1 EC1-353 , online - Zoom	Thursday, Feb 13, 13:15-17:00	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,
	Friday, Feb 14, 9:15-12:00	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,
	Friday, Feb 14, 13:15-16:00	Discussion and problem solving session	CANCELED !
2 EC1-353 , online - Zoom	Thursday, March 6, 13:15-16:00	General theory of estimation. Consistency and efficiency.	Section 3.4 and 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,
	Friday, March 7, 9:15-12:00	Testing hypothesis and the Neyman-Pearson lemma. Uniformly most powerful tests, Confidence regions.	Section 4.1-2, Sections 4.3-5 of the text Lecture 6 Slides Lecture 7 Slides and Lecture 8 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, 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,
	Friday, March 7, 13:15-17:00	Discussion and problem solving session
3 EC1-353 , online - Zoom	Thursday, March 13, 9:15-12:00	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
	Thursday, March 13, 13:15-16:00	Likelihood ratio procedures, Asymptotical Consistency, Discussion	Section 4.9.1-4 Section 5.2.1 Lecture 11 Slides	Some comments and tips
	Friday, March 14, 13:15-17:00	Discussion and problem solving session	Cancelled, see also below for a change of the requirements for passing grades.
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 are included in the slides. You are expected to deliver a single file with attempts on solutions to all these problems. The due date is April 16.

Activity Due to challenges in stimulation of discussions with online sessions, there is no requirement on activity. However, to facilitate opportunities for conversation, please feel free to contact Krzysztof Podgorski to discuss any topic or problem from the first part of the course.