# Course: Statistics 2

Course type: compulsory
Lecturer: Assoc Prof Mihael Perman, Assoc Prof Jaka Smrekar

Study programme and level Study field Academic year Semester
Applied statistics, second level Mathematical Statistics 1st 2nd

For the timeline see Curriculum.

Prerequisites:

• Enrolment into the first year of the programme is required to participate in the course.
• Prerequisits to the written exam are the successfully completed homeworks.

Content (Syllabus outline):

• Linear methods for data analysis:  Linear regression, multiple and partial correlation coefficients), canonical correlation analysis, least square estimators, Gauss-Markov theorem, canonical reduction of the linear model, hypothesis testing, prediction, generalizations of linear regression.
• Analysis of variance: One factor classification, two-factor classification, test of significance.
• Parameter estimation: consistency, completeness, unbiased estimators, efficient estimators, best linear estimator, Rao-Cramer boundary, maximum likelihood method, minimax method, asymptotical properties of estimators.
• Testing of hypotheses: Fundamentals (probablistic and nonprobalistic hypotheses, types of errors, best tests). Neyman-Pearson lemma, uniformly most powerfull tests, test in general parametric models, Wilks theorem, non-parametric tests.
• Confidence intervals:  Constructions, pivots, properties of confidence regions, asymptotic properties, the bootstrap.
• Multivariate analysis:  Principal component analysis,  factor analysis, discriminant analysis, classification mathods.
• Basic Bayesian statistics:  Bayes formula, data, likelihood, apriori and aposteriory distributions, conjugate distributions pairs,  Bayesian parameter estimation, Bayesian hyposthesis testing.

Objectives and competences:

Theoretical basis for the statistical modeling will be presented. Deeper mathematical methods are needed for well grounded statistical applications. Fundamentals of Bayesian analysis will be presented.

Intended learning outcomes:

Understanding of statistical applications, interplay between statistical  reasoning and models.

### Contact

Main contact:
e-mail: info.stat (at) uni-lj.si

Contact for administrative questions (enrolment, technical questions):
Katarina Erjavec Drešar
University of Ljubljana, Faculty of electrical engineering, Tržaška cesta 25, 1000 Ljubljana.
room num.: AN012C-ŠTU
phone: 01 4768 209
e-mail: katarina.erjavec-dresar (at) fe.uni-lj.si