Statistics 2

There are no prerequisites.

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.

1. D. R. Cox, D. V. Hinkley: Theoretical statistics, Boca Raton [etc.] : Chapman & Hall/CRC, 2000.
2. A. Gelman … [et al.]: Bayesian data analysis, 2nd ed., Boca Raton : Chapman & Hall/CRC, cop. 2004.
3. K. V. Mardia, J. T. Kent, J. M. Bibby: Multivariate Analysis, Amsterdam : Academic, 2003, cop. 1979.
4. J. Rice: Mathematical statistics and data analysis, 3rd ed., Belmont (CA) : Thomson/Brooks/Cole, cop. 2007.
5. G. G. Roussas: A course in mathematical statistics, 2nd ed., San Diego : Academic Press, cop. 1997.
6. S. Weisberg: Applied Linear Regression, 3rd ed., Hoboken (New Jersey) : J. Wiley & Sons, cop. 2005.

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.

Knowledge and understanding:
Understanding of statistical applications to economics, interplay between statistical reasoning and economics.
Application:
Statistics is the language of the quantitative economics. On one side, application is immediate, on the other side the knowledge will satisfy to persue doctoral studies in economics.
Reflection:
The interplay between application, statistical modelling, economics feedback information, and application stimulation for mathematical reasoning.
Transferable skills:
The skills obtained are transferable to other areas of mathematical modelling, but the gist of the course is its immediate applicability.

lectures, tutorials, 2 individual projects

2 midterm exams instead of written exam, written exam
Oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Mihael Perman:
BLEJEC, Matjaž, LOVREČIČ SARAŽIN, Marko, PERMAN, Mihael, ŠTRAUS, Mojca. Statistika. Piran: Gea College, Visoka šola za podjetništvo, 2003. X, 150 str., graf. prikazi, tabele. ISBN 961-6347-43-8. [COBISS-SI-ID 122243328]
PERMAN, Mihael. Order statistics for jumps of normalised subordinators. Stochastic Processes and their Applications, ISSN 0304-4149. [Print ed.], 1993, vol. 46, no. 2, str. 267-281. [COBISS-SI-ID 12236633]
HUZAK, Miljenko, PERMAN, Mihael, ŠIKIĆ, Hrvoje, VONDRAČEK, Zoran. Ruin probabilities and decompositions for general perturbed risk processes. Annals of applied probability, ISSN 1050-5164, 2004, vol. 14, no. 3, str. 1378-1397. [COBISS-SI-ID 13168985]
Jaka Smrekar:
SMREKAR, Jaka. Homotopy type of space of maps into a K(G,n). Homology, homotopy, and applications, ISSN 1532-0073, 2013, vol. 15, no. 1, str. 137-149. [COBISS-SI-ID 16643929]
SMREKAR, Jaka. Turning a self-map into a self-fibration. Topology and its Applications, ISSN 0166-8641. [Print ed.], 2014, vol. 167, str. 76-79. [COBISS-SI-ID 16943705]
SMREKAR, Jaka. Homotopy type of mapping spaces and existence of geometric exponents. Forum mathematicum, ISSN 0933-7741, 2010, vol. 22, no. 3, str. 433-456. [COBISS-SI-ID 15638105]