Completed courses Analysis 2, Probability and statistics and Probability 1.
Statistics 1
2023/2024
Programme:
Financial mathematics, First Cycle
Year:
3 year
Semester:
second
Kind:
mandatory
ECTS:
5
Language:
slovenian
Course director:
Lecturer (contact person):
Hours per week – 2. semester:
Lectures
2
Seminar
0
Tutorial
2
Lab
0
Content (Syllabus outline)
Survey of statistical models, linear regression, analysis of variance, logistic regression, multivariate methods, time series, nonparametric methods, generalized linear models.
Sufficiency, definition, Rao-Blackwell factorization theorem, uniformly best estimators, Neyman-Pearson theorem, uniformly most powerfull tests.
Nonparametric methods.
Multivariate normal distribution, definition, properties, conditional distributions, quadratic forms.
Regression, estimation of linear functionals, general Gauss-Markov theorem, generalizations.
Readings
J. Rice, Mathematical Statistics & Data Analysis, Third Edition, Duxburry, 2007.
G. G. Roussas, A Course in Mathematical Statistics, 2nd edition, Academic Press, 1997.
Objectives and competences
Analysing and interpreting data is an essential part of the work of a financial mathematician. The course presents more advanced statistical concepts and statistical models most commonly used in statistical practice.
Intended learning outcomes
Introduction of statistical concepts sufficient for independent study and the ability to present and analyze data with more advanced statistical models.
Learning and teaching methods
Lectures, problem sessions, seminar assignment.
Assessment
2 midterms or written exam, oral exam.
Seminar assignment.
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)
Lecturer's references
PERMAN, Mihael. An excursion approach to Ray-Knight theorems for perturbed Brownian motion. Stochastic Processes and their Applications, ISSN 0304-4149. [Print ed.], 1996, let. 63, str. 67-74. [COBISS-SI-ID 7621465]
PERMAN, Mihael, WELLNER, Jon A. On the distribution of Brownian areas. Annals of applied probability, ISSN 1050-5164, 1996, let. 6, št. 4, str. 1091-1111. [COBISS-SI-ID 7101017]
PERMAN, Mihael, WELLNER, Jon A. An excursion approach to maxima of the Brownian bridge. Stochastic Processes and their Applications, ISSN 0304-4149. [Print ed.], 2014, vol. 124, iss. 9, str. 3106-3120. [COBISS-SI-ID 17154393]
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 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. 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]
