Course content

Transformations and moments of random variables. Families of distributions. Inequalities and convergence theorems. Sufficient statistics. Frequentist and Bayesian estimators. Methods of constructing point estimators, interval estimators and hypothesis tests, and optimality of these. Asymptotic properties of estimators and hypothesis tests.

Learning outcome

1. Knowledge. The student has basic theoretical knowledge about fundamental principles
for statistical inference. The student has knowledge about construction of point and interval
estimators, and hypothesis testing; and about the evaluation of these estimators and tests.
The student has insight in how to construct optimal estimators and tests. Moreover, the
student has some knowledge about asymptotic theory for statistical inference.
2. Skills. The student can perform point estimation, hypothesis testing and interval estimation
under a large variety of discrete and continuous probability models. Further, the student
can evaluate the properties of these estimators and tests, for both finite sample sizes and
asymptotically as the sample size tends to infinity. Lastly, the student can select optimal
estimators.

Learning methods and activities

Lectures and exercises. Written final examination is the basis for the grade awarded in the course. Retake of examination may be given as an oral examination. The lectures may be given in English. If the course is taught in English, the exam will be given only in English. Students are free to choose Norwegian or English for written assessments.

Recommended previous knowledge

TMA4240/4245 Statistics or equivalent. The course demands some degree of maturity in
Statistics and we also recommend to have TMA4267 Linear Statistical Models or TMA4255
Applied Statistics.

Course materials

Will be announced at the start of the semester.

Credit reductions