Statistics 2

2022/2023
Programme:
Financial Mathematics, Second cycle
Year:
1 ali 2 year
Semester:
first or second
Kind:
core mandatory
Group:
M5
ECTS:
6
Language:
slovenian, english
Hours per week – 1. or 2. semester:
Lectures
3
Seminar
0
Tutorial
2
Lab
0
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.

Readings

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.

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

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.

Learning and teaching methods

lectures, tutorials, 2 individual projects

Assessment

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

Lecturer's references

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]