# Statistics 2

## Subject description

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, unbiasedness estimators, efficient estimators, best linearcy, uniformly minimum variance unbiased estimator, Rao-Cramer boundary, the method of maximum likelihood method, minimax method, asymptotical properties of estimators.

Testing of hypotheses: Fundamentals (probablistic and nonprobalistic hypotheses, types of errors, the power of a testbest tests). Uniformly most powerful tests, Neyman-Pearson’s lemma, uniformly most powerfull tests, test in general parametric models, Wilks' theorem, non-parametric tests.

Confidence intervals: Constructions, pivotal quantities, properties of confidence regions, asymptotic properties, the bootstrap.

Multivariate analysis: Principal component analysis, factor analysis, discriminant analysis, classification meathods.

Basic Bayesian statistics: Bayes formula, data, likelihood, apriori and aposteriory distributions, conjugate distributions pairs, Bayesian parameter estimation, Bayesian hyposthesis testing.

## Objectives and competences

A theoretical basis for the statistical modelling will be presented. Some advanced mathematics are needed for well grounded statistical applications.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.

## Teaching and learning methods

lectures, tutorials, 2 individual projects

Part of the pedagogical process will be carried out with the help of ICT technologies and the opportunities they offer.

## Expected study results

Knowledge and understanding:

Understanding the concept of a statistical model; mathematical background of modelling, estimation, and testingUnderstanding of statistical applications, interplay between statistical reasoning and models.

Application:

A theoretical basis of statistics strengthens the ability of statistical thinking in all fields of application.A theoretical basis of statistics strengthens the ability of statistical thinking and understanding of the basical ideas in any field of statistics..

Reflection:

The interplay between application, statistical modelling, economics feedback information from other fields, and application stimulation for mathematical reasoning.

Transferable skills:

The skills obtained are transferable to all fields of statistics since the basic ideas of statistics form represent a common grounds forin all fields. The understanding of these ideas simplifies the study of specific methods of any field.

## Basic sources and literature

• A. Gelman, J.B.Carlin, H.S. Stern, D.B. Rubin: Bayesian Data Analysis. 2nd edition,  Chapman&Hall, 1995.
• J. Rice: Mathematical Statistics and Data Analysis, Second edition, Duxbury Press, 1995.
• G.G. Roussas: A course in mathematical statistics, 2nd edition, Academic Press, 1997.
• D. R. Cox, D. V. Hinkley: Theoretical Statistics, Chapman & Hall/ CRC, 2000.
• S. Weisberg, Applied Linear Regression: 3rd edition,  Wiley, 2005.
• K. V. Mardia, J. T. Kent, J. M. Bibby: Multivariate Analysis, Academic Press, 1979.

## Stay up to date

University of Ljubljana, Faculty of Electrical Engineering Tržaška cesta 25, 1000 Ljubljana