# Course: Introduction to Theoretical Statistics

Course type: compulsory

Lecturer: Maja Pohar Perme, Ph.D., Associate Professor

Study programme and level | Study field | Academic Year | Semester |
---|---|---|---|

Applied statistics, second level | All modules | 1st | 1st and 2nd |

For the timeline see Curriculum.

Prerequisites:

- Enrolment into the first year of the programme.
- Prerequisites to the written exam are successfully completed homeworks.

Content (Syllabus outline):

- Overview of descriptive statistics, basic graphical methods, examples.
- Sampling, sampling design, sampling distribution, standard error, confidence intervals, examples.
- Definition and goal of statistical model, examples.
- Parameter estimation, maximum likelihood method, estimator properties, asymptotical distributions, alternative methods for parameter estimations, examples.
- Hypotheses testing, test power, methods for test statistics, analysis of variance, independence tests, asymptotical properties, nonparametric tests, goodness of fit tests, examples.
- Linear regression, least squares method, Gauss-Markov theorem, inference.
- Generalized linear models, probit, logit, examples.
- Basic ideas of Bayesian statistics.

Objectives and competences:

The course presents the basic statistical ideas and their theoretical background. Theoretical concepts are illustrated on the examples of commonly used methods, tests and models. At the end of the course, the student shall be able to present the problem theoretically, to choose the appropriate methods and to understand the results, assumptions and restrictions.

Intended learning outcomes:

Understanding of the theoretical framework of the statistical ideas. The course presents basic statistical ideas that form the basis for all fields of statistics and overviews the most frequently used methods.