STK9090 – Statistical large-sample theory
Course description
Schedule, syllabus and examination date
Course content
Important parts of statistical theory and its applications build on approximations to the most relevant distributions, and these approximations are valid when the sample size is large. This course deals with the machinery of such large-sample approximations, including the basics of probability theory; the laws of large numbers; convergence in probability and in distribution; characteristic functions; central limit theorems. There will be applications to studying maximum likelihood and Bayes procedures. The course also involves limit and approximation theorems for classes of empirical processes. The theory is being illustrated by statistical applications.
Learning outcome
By completing the course, you will
- know how to construct approximations to the distributions of important classes of estimators and test statistics
- be able to build confidence intervals and confidence curves based on such approximations
- have learned basic limit theorems and techniques associated with limiting normality and associated distributions
- have understood classes of empirical processes and their limits, involving Brownian motion
- have worked with non-trivial statistical applications of the general large-sample theory.
Admission to the course
PhD candidates from the Faculty of Mathematics and Natural Sciences at the University of Oslo should apply for classes and register for examinations through Studentweb.
If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.
PhD candidates who have been admitted to another higher education institution must apply for a position as a visiting student within a given deadline.
Recommended previous knowledge
It is strongly recommended to have taken STK4011 – Statistical Inference Theory.
In addition:
- STK1100 – Probability and Statistical Modelling
- STK1110 – Statistical Methods and Data Analysis
- MAT2400 – Real Analysis
Overlapping courses
- 10 credits overlap with STK4090 – Statistical large-sample theory.
Teaching
4 hours of lectures/exercises per week throughout the semester.
The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.
Upon the attendance of three or fewer students, the lecturer may, in conjunction with the Head of Teaching, change the course to self-study with supervision.
Examination
Depending on the number of students, the exam will be in one of the following four forms:
- Final written exam, which counts 100% for censorship.
- Final oral exam, which counts 100% for censorship.
- Project assignment and final written examination, which are emphasized equally in the assessment. Both exam parts must be passed in the same semester.
- Project assignment and final oral examination, which are emphasized equally in the assessment. Both exam parts must be taken in the same semester. ?
The form of examination will be announced by the teaching staff by 1 October/1 March for?the autumn semester and the spring semester respectively.
In addition, each PhD?candidate is expected to give a?one hour oral presentation on a topic of relevance chosen in cooperation with the lecturer. The presentation has to be approved by the lecturer for the student to be admitted to the final exam.
It will also be counted as one of the three attempts to sit the exam for this course, if you sit the exam for one of the following courses: STK4090 – Statistical large-sample theory
Examination support material
No examination support material is allowed.
Language of examination
Courses taught in English will only offer the exam paper in English. You may write your examination paper in Norwegian, Swedish, Danish or English.
Grading scale
Grades are awarded on a pass/fail scale. Read more about the grading system.
Resit an examination
This course offers both postponed and resit of examination. Read more:
More about examinations at UiO
- Use of sources and citations
- Special exam arrangements due to individual needs
- Withdrawal from an exam
- Illness at exams / postponed exams
- Explanation of grades and appeals
- Resitting an exam
- Cheating/attempted cheating
You will find further guides and resources at the web page on examinations at UiO.