Statistical Inference

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.

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.

Lectures and compulsory exercises. Written final exam is the basis for the grade awarded in the exam. Specific exercises has to be approved in order to be allowed to take the exam.

Students are free to choose Norwegian or English for written assessments.