CLICK HERE FOR THE COURSE SYLLABUS (.pdf)


COURSE INTRODUCTION AND APPLICATION INFORMATION

 
Course Name
Code
Semester
Theory
(hour/week)
Application/Laboratory
(hour/week)
Local Credits
ECTS
Multivariate Statistics and the Theory of Copulas
STAT 506
Fall/Spring
3
0
3
7.5

Prerequisites
None

Course Language
English
Course Type
Elective
Course Level
Second Cycle
Course Coordinator -
Course Lecturer(s) -
Course Assistants -
Course Objectives This course aims to provide some systems of continuous and discrete multivariate distributions. Some multivariate statistical techniques also will be studied. The concept of copula will be introduced and dependence and ageing properties of random variables will be studied with the help of copulas.
Course Learning Outcomes The students who succeeded in this course;
  • will be able to understand and implement some common multivariate methods.
  • will be able to choose an appropriate method for a given data set and problem.
  • will be able to use copulas for modelling dependence.
  • will be able to analyse the lifetime properties of copulas.
Course Content The course is designed to provide graduate students in mathematics and statistics with a strong grasp of the multivariate statistical theory, particularly emphasizing the connection with the theory of copulas.

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Related Preparation
1 Copulas, Sklar’s Theorem, Copulas and Random Variables “Multivariate Statistical Methods”, Donald F. MORRISON, McGrawHill, 1990.“An Introduction to Copulas”, Roger B. NELSON, Springer Series in Statistics, 2006.
2 The Frechet – Hoeffding Bounds for Joint Distribution Functions of Random Variables “Multivariate Statistical Methods”, Donald F. MORRISON, McGrawHill, 1990.“An Introduction to Copulas”, Roger B. NELSON, Springer Series in Statistics, 2006..
3 Survival Copulas, Multivariate Copulas, “Multivariate Statistical Methods”, Donald F. MORRISON, McGrawHill, 1990.“An Introduction to Copulas”, Roger B. NELSON, Springer Series in Statistics, 2006..
4 Archimedean copulas “Multivariate Statistical Methods”, Donald F. MORRISON, McGrawHill, 1990.“An Introduction to Copulas”, Roger B. NELSON, Springer Series in Statistics, 2006.
5 Methods of Constructing Copulas. “Multivariate Statistical Methods”, Donald F. MORRISON, McGrawHill, 1990.“An Introduction to Copulas”, Roger B. NELSON, Springer Series in Statistics, 2006.
6 The Multivariate Normal Distribution, “Multivariate Statistical Methods”, Donald F. MORRISON, McGrawHill, 1990.“An Introduction to Copulas”, Roger B. NELSON, Springer Series in Statistics, 2006..
7 Distribution of the Quadratic Form of the Multivariate Normal Density “Multivariate Statistical Methods”, Donald F. MORRISON, McGrawHill, 1990.“An Introduction to Copulas”, Roger B. NELSON, Springer Series in Statistics, 2006.
8 Multivariate Exponential Distributions. “Multivariate Statistical Methods”, Donald F. MORRISON, McGrawHill, 1990.“An Introduction to Copulas”, Roger B. NELSON, Springer Series in Statistics, 2006.
9 The Wishart Distribution, Partitioning the x vector and Conditional Covariance Matrices “Multivariate Statistical Methods”, Donald F. MORRISON, McGrawHill, 1990.“An Introduction to Copulas”, Roger B. NELSON, Springer Series in Statistics, 2006.
10 Multivariate Gamma distribution “Multivariate Statistical Methods”, Donald F. MORRISON, McGrawHill, 1990.“An Introduction to Copulas”, Roger B. NELSON, Springer Series in Statistics, 2006.
11 Dependence and ageing properties of random variables in terms of copulas. “Multivariate Statistical Methods”, Donald F. MORRISON, McGrawHill, 1990.“An Introduction to Copulas”, Roger B. NELSON, Springer Series in Statistics, 2006.
12 Kendall's tau, Sperman's rho. Tail monotonicity. “Multivariate Statistical Methods”, Donald F. MORRISON, McGrawHill, 1990.“An Introduction to Copulas”, Roger B. NELSON, Springer Series in Statistics, 2006.
13 Other measures of Association. Measures based on Gini's Coefficient. “Multivariate Statistical Methods”, Donald F. MORRISON, McGrawHill, 1990.“An Introduction to Copulas”, Roger B. NELSON, Springer Series in Statistics, 2006.
14 Empirical copulas “Multivariate Statistical Methods”, Donald F. MORRISON, McGrawHill, 1990.“An Introduction to Copulas”, Roger B. NELSON, Springer Series in Statistics, 2006.
15 Multivariate dependence “Multivariate Statistical Methods”, Donald F. MORRISON, McGrawHill, 1990.“An Introduction to Copulas”, Roger B. NELSON, Springer Series in Statistics, 2006.
16 Review of the Semester  

 

SOURCES

Course Notes / Textbooks “Multivariate Statistical Methods”, Donald F. MORRISON, McGrawHill, 1990.“An Introduction to Copulas”, Roger B. NELSON, Springer Series in Statistics, 2006.
References Multivariate Analysis, K. V. MARDIA, J. T. KENT and J. M. BIBBY, Academic Press, 1979.

 

EVALUATION SYSTEM

Semester Requirements Number Percentage of Grade
Attendance/Participation
Laboratory
Application
Field Work
Special Course Internship (Work Placement)
Quizzes/Studio Critics
Homework Assignments
Presentation/Jury
Project
1
20
Seminar/Workshop
Midterms/Oral Exams
1
30
Final/Oral Exam
1
50
Total

PERCENTAGE OF SEMESTER WORK
50
PERCENTAGE OF FINAL WORK
50
Total

 

COURSE CATEGORY

Course Category

Core Courses
Major Area Courses
X
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

 

THE RELATIONSHIP BETWEEN COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS

#
Program Qualifications / Outcomes
* Level of Contribution
1
2
3
4
5
1

To develop and deepen his/her knowledge on theories of mathematics and statistics and their applications in level of expertise, and to obtain unique definitions which bring innovations to the area, based on master level competencies,

X
2

To have the ability of original, independent and critical thinking in Mathematics and Statistics and to be able to develop theoretical concepts,

X
3

To have the ability of defining and verifying problems in Mathematics and Statistics,

X
4

With an interdisciplinary approach, to be able to apply theoretical and applied methods of mathematics and statistics in analyzing and solving new problems and to be able to discover his/her own potentials with respect to the application,

X
5

In nearly every fields that mathematics and statistics are used, to be able to execute, conclude and report a research, which requires expertise, independently,

X
6

To be able to evaluate and renew his/her abilities and knowledge acquired in the field of Applied Mathematics and Statistics with critical approach, and to be able to analyze, synthesize and evaluate complex thoughts in a critical way,

X
7

To be able to convey his/her analyses and methods in the field of Applied Mathematics and Statistics to the experts in a scientific way,

X
8

To be able to use national and international academic resources (English) efficiently, to update his/her knowledge, to communicate with his/her native and foreign colleagues easily, to follow the literature periodically, to contribute scientific meetings held in his/her own field and other fields systematically as written, oral and visual.

X
9

To be familiar with computer software commonly used in the fields of Applied Mathematics and Statistics and to be able to use at least two of them efficiently,

X
10

To contribute the transformation process of his/her own society into an information society and the sustainability of this process by introducing scientific, technological, social and cultural advances in the fields of Applied Mathematics and Statistics,

X
11

As having rich cultural background and social sensitivity with a global perspective, to be able to evaluate all processes efficiently, to be able to contribute the solutions of social, scientific, cultural and ethical problems and to support the development of these values,

X
12

As being competent in abstract thinking, to be able to connect abstract events to concrete events and to transfer solutions, to analyze results with scientific methods by designing experiment and collecting data and to interpret them,

X
13

To be able to produce strategies, policies and plans about systems and topics in which mathematics and statistics are used and to be able to interpret and develop results,

X
14

To be able to evaluate, argue and analyze prominent persons, events and phenomena, which play an important role in the development and combination of the fields of Mathematics and Statistics, within the perspective of the development of other fields of science,

X
15

In Applied Mathematics and Statistics, to be able to sustain scientific work as an individual or a group, to be effective in all phases of an independent work, to participate decision-making process and to make and execute necessary planning within an effective time schedule.

X

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

ECTS / WORKLOAD TABLE

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
16
3
Laboratory
Application
Special Course Internship (Work Placement)
Field Work
Study Hours Out of Class
15
6
Presentations / Seminar
Project
1
22
Homework Assignments
Quizzes
Midterms / Oral Exams
1
30
Final / Oral Exam
1
35
    Total Workload

CLICK HERE FOR THE COURSE SYLLABUS (.pdf)

 
 

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