GRADUATE SCHOOL
PH.D. In Applied Mathematics and Statistics
STAT 506 | Course Introduction and Application Information
| Course Name |
Multivariate Statistics and the Theory of Copulas
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|
Code
|
Semester
|
Theory
(hour/week) |
Application/Lab
(hour/week) |
Local Credits
|
ECTS
|
|
STAT 506
|
Fall/Spring
|
3
|
0
|
3
|
7.5
|
| Prerequisites |
None
|
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| Course Language |
English
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| Course Type |
Elective
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| Course Level |
Second Cycle
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| Mode of Delivery | - | |||||
| Teaching Methods and Techniques of the Course | - | |||||
| Course Coordinator | - | |||||
| Course Lecturer(s) | ||||||
| Assistant(s) | - | |||||
| 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. |
| Learning Outcomes |
The students who succeeded in this course;
|
| Course Description | 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. |
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Core Courses | |
| Major Area Courses |
X
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|
| Supportive Courses | ||
| Media and Management Skills Courses | ||
| Transferable Skill Courses |
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, Duxbury Press; 4 edition,2004. ISBN-13: 978-0534387785 “An Introduction to Copulas”, Roger B. NELSON, Springer; 2nd edition,2006. ISBN-13: 978-0387286594 |
| 2 | The Frechet – Hoeffding bounds for joint distribution functions of random variables | “Multivariate Statistical Methods”, Donald F. MORRISON, Duxbury Press; 4 edition,2004. ISBN-13: 978-0534387785 “An Introduction to Copulas”, Roger B. NELSON, Springer; 2nd edition,2006. ISBN-13: 978-0387286594 |
| 3 | Survival copulas, multivariate copulas | “Multivariate Statistical Methods”, Donald F. MORRISON, Duxbury Press; 4 edition,2004. ISBN-13: 978-0534387785 “An Introduction to Copulas”, Roger B. NELSON, Springer; 2nd edition,2006. ISBN-13: 978-0387286594 |
| 4 | Archimedean copulas | “Multivariate Statistical Methods”, Donald F. MORRISON, Duxbury Press; 4 edition,2004. ISBN-13: 978-0534387785 “An Introduction to Copulas”, Roger B. NELSON, Springer; 2nd edition,2006. ISBN-13: 978-0387286594 |
| 5 | Methods of constructing copulas | “Multivariate Statistical Methods”, Donald F. MORRISON, Duxbury Press; 4 edition,2004. ISBN-13: 978-0534387785 “An Introduction to Copulas”, Roger B. NELSON, Springer; 2nd edition,2006. ISBN-13: 978-0387286594 |
| 6 | The multivariate normal distribution | “Multivariate Statistical Methods”, Donald F. MORRISON, Duxbury Press; 4 edition,2004. ISBN-13: 978-0534387785 “An Introduction to Copulas”, Roger B. NELSON, Springer; 2nd edition,2006. ISBN-13: 978-0387286594 |
| 7 | Distribution of the quadratic form of the multivariate normal density | “Multivariate Statistical Methods”, Donald F. MORRISON, Duxbury Press; 4 edition,2004. ISBN-13: 978-0534387785 “An Introduction to Copulas”, Roger B. NELSON, Springer; 2nd edition,2006. ISBN-13: 978-0387286594 |
| 8 | Multivariate exponential distributions | “Multivariate Statistical Methods”, Donald F. MORRISON, Duxbury Press; 4 edition,2004. ISBN-13: 978-0534387785 “An Introduction to Copulas”, Roger B. NELSON, Springer; 2nd edition,2006. ISBN-13: 978-0387286594 |
| 9 | The Wishart distribution, partitioning the x vector and conditional covariance matrices | “Multivariate Statistical Methods”, Donald F. MORRISON, Duxbury Press; 4 edition,2004. ISBN-13: 978-0534387785 “An Introduction to Copulas”, Roger B. NELSON, Springer; 2nd edition,2006. ISBN-13: 978-0387286594 |
| 10 | Multivariate gamma distribution | “Multivariate Statistical Methods”, Donald F. MORRISON, Duxbury Press; 4 edition,2004. ISBN-13: 978-0534387785 “An Introduction to Copulas”, Roger B. NELSON, Springer; 2nd edition,2006. ISBN-13: 978-0387286594 |
| 11 | Dependence and ageing properties of random variables in terms of copulas | “Multivariate Statistical Methods”, Donald F. MORRISON, Duxbury Press; 4 edition,2004. ISBN-13: 978-0534387785 “An Introduction to Copulas”, Roger B. NELSON, Springer; 2nd edition,2006. ISBN-13: 978-0387286594 |
| 12 | Kendall's tau, Sperman's rho. Tail monotonicity | “Multivariate Statistical Methods”, Donald F. MORRISON, Duxbury Press; 4 edition,2004. ISBN-13: 978-0534387785 “An Introduction to Copulas”, Roger B. NELSON, Springer; 2nd edition,2006. ISBN-13: 978-0387286594 |
| 13 | Other measures of association. Measures based on Gini's coefficient | “Multivariate Statistical Methods”, Donald F. MORRISON, Duxbury Press; 4 edition,2004. ISBN-13: 978-0534387785 “An Introduction to Copulas”, Roger B. NELSON, Springer; 2nd edition,2006. ISBN-13: 978-0387286594 |
| 14 | Empirical copulas, multivariate dependence | “Multivariate Statistical Methods”, Donald F. MORRISON, Duxbury Press; 4 edition,2004. ISBN-13: 978-0534387785 “An Introduction to Copulas”, Roger B. NELSON, Springer; 2nd edition,2006. ISBN-13: 978-0387286594 |
| 15 | Semester review | |
| 16 | Final exam |
| Course Notes/Textbooks | “Multivariate Statistical Methods”, Donald F. MORRISON, Duxbury Press; 4 edition,2004. ISBN-13: 978-0534387785 “An Introduction to Copulas”, Roger B. NELSON, Springer; 2nd edition,2006. ISBN-13: 978-0387286594
|
| Suggested Readings/Materials | Multivariate Analysis, K. V. MARDIA, J. T. KENT and J. M. BIBBY, Academic Press, 1979. ISBN-13: 978-0124712522 |
EVALUATION SYSTEM
| Semester Activities | Number | Weigthing |
| Participation | ||
| Laboratory / Application | ||
| Field Work | ||
| Quizzes / Studio Critiques | ||
| Portfolio | ||
| Homework / Assignments | ||
| Presentation / Jury | ||
| Project |
1
|
20
|
| Seminar / Workshop | ||
| Oral Exams | ||
| Midterm |
1
|
30
|
| Final Exam |
1
|
50
|
| Total |
| Weighting of Semester Activities on the Final Grade |
50
|
|
| Weighting of End-of-Semester Activities on the Final Grade |
50
|
|
| Total |
ECTS / WORKLOAD TABLE
| Semester Activities | Number | Duration (Hours) | Workload |
|---|---|---|---|
| Theoretical Course Hours (Including exam week: 16 x total hours) |
16
|
3
|
48
|
| Laboratory / Application Hours (Including exam week: '.16.' x total hours) |
16
|
0
|
|
| Study Hours Out of Class |
14
|
6
|
84
|
| Field Work |
0
|
||
| Quizzes / Studio Critiques |
0
|
||
| Portfolio |
0
|
||
| Homework / Assignments |
0
|
||
| Presentation / Jury |
0
|
||
| Project |
1
|
28
|
28
|
| Seminar / Workshop |
0
|
||
| Oral Exam |
0
|
||
| Midterms |
1
|
30
|
30
|
| Final Exam |
1
|
35
|
35
|
| Total |
225
|
COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP
|
#
|
Program Competencies/Outcomes |
* Contribution Level
|
||||
|
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
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