| Course Name | Theory of Statistics |
| Code | Semester | Theory (hour/week) | Application/Lab (hour/week) | Local Credits | ECTS |
|---|---|---|---|---|---|
| MATH 304 | Spring | 3 | 0 | 3 | 7 |
| Prerequisites | None | |||||
| Course Language | English | |||||
| Course Type | Required | |||||
| Course Level | First Cycle | |||||
| Mode of Delivery | face to face | |||||
| Teaching Methods and Techniques of the Course | ||||||
| Course Coordinator | - | |||||
| Course Lecturer(s) | ||||||
| Assistant(s) | ||||||
| Course Objectives | This course objective is to make the students familiar with the basics of the theory and applications of mathematical statistics. |
| Learning Outcomes | The students who succeeded in this course;
|
| Course Description | In this course, the concepts of the sample population, lthe ikelihood and invariance princeples, point estimation, hypothesis testing, interval estimation and the decision theory are discussed. |
| Related Sustainable Development Goals | |
|
| Core Courses | X |
| Major Area Courses | ||
| Supportive Courses | ||
| Media and Managment Skills Courses | ||
| Transferable Skill Courses |
| Week | Subjects | Required Materials |
| 1 | Introduction to basic concepts of statistics. Sampling from infinite population, simple random sample, stratified sample, cluster sampling, systematic sample | “Statistical Inference” by G. Casella, R. L. Berger, Duxbury Press,1990, ISBN-13:9780534243128. section 5.1. |
| 2 | Properties of random sample | “Statistical Inference” by G. Casella, R. L. Berger, Duxbury Press,1990, ISBN-13:9780534243128. section 5.2. |
| 3 | Order statics, Stieltjes integral | “Statistical Inference” by G. Casella, R. L. Berger, Duxbury Press,1990, ISBN-13:9780534243128. section 5.3. |
| 4 | Emprical distribution function, Glivenko-Cantelli theorem | “Statistical Inference” by G. Casella, R. L. Berger, Duxbury Press,1990, ISBN-13:9780534243128. section 5.4., “Mathematical Statistics” by A. A. Borovkov, Gordon and Breach Science Publishers,1998, ISBN:90-5699-018-7. +Section 1.2-1.3 |
| 5 | Two types of statistics | “Statistical Inference” by G. Casella, R. L. Berger, Duxbury Press,1990, ISBN-13:9780534243128. section 6., “Mathematical Statistics” by A. A. Borovkov, Gordon and Breach Science Publishers,1998, ISBN:90-5699-018-7. Section 1.5 |
| 6 | Continuity theorems for two types of statistics | “Statistical Inference” by G. Casella, R. L. Berger, Duxbury Press,1990, ISBN-13:9780534243128. section 7.1., “Mathematical Statistics” by A. A. Borovkov, Gordon and Breach Science Publishers,1998, ISBN:90-5699-018-7. Section 1.5-1.7 |
| 7 | Point estimation, principles of data reduction | “Statistical Inference” by G. Casella, R. L. Berger, Duxbury Press,1990, ISBN-13:9780534243128. section 7.2. |
| 8 | Methods of moments | “Statistical Inference” by G. Casella, R. L. Berger, Duxbury Press,1990, ISBN-13:9780534243128. section 7.2. |
| 9 | Regression analysis:Maximum likelihood estimators of regression parameters | “Statistical Inference” by G. Casella, R. L. Berger, Duxbury Press,1990, ISBN-13:9780534243128. Section 11.3 & 12.2.3. |
| 10 | Midterm I | |
| 11 | Methods of evaluating estimators, consistency of estimators | “Statistical Inference” by G. Casella, R. L. Berger, Duxbury Press,1990, ISBN-13:9780534243128. section 7.3. |
| 12 | Midterm II | |
| 13 | Nonparametric estimation, hypothesis testing | “Statistical Inference” by G. Casella, R. L. Berger, Duxbury Press,1990, ISBN-13:9780534243128. section 8. |
| 14 | Likelihood ratio test, Neyman-Pearson lemma, regression analysis, Least square method | “Statistical Inference” by G. Casella, R. L. Berger, Duxbury Press,1990, ISBN-13:9780534243128. section 8.2.1. |
| 15 | Semester review | - |
| 16 | Final exam | - |
| Course Notes/Textbooks | “Statistical Inference” by G. Casella, R. L. Berger, Duxbury Press,1990, ISBN-13:9780534243128. “Mathematical Statistics” by A. A. Borovkov, Gordon and Breach Science Publishers,1998, ISBN:90-5699-018-7. |
| Suggested Readings/Materials | “Mathematical Statistics” by J. Shao, Springer.; 2nd edition, 2003,ISBN-13:978-0387953823 |
| Semester Activities | Number | Weigthing |
| Participation | ||
| Laboratory / Application | ||
| Field Work | ||
| Quizzes / Studio Critiques | - | - |
| Portfolio | ||
| Homework / Assignments | - | - |
| Presentation / Jury | ||
| Project | ||
| Seminar / Workshop | ||
| Oral Exam | ||
| Midterm | 1 | 40 |
| Final Exam | 1 | 60 |
| Total |
| Weighting of Semester Activities on the Final Grade | 1 | 40 |
| Weighting of End-of-Semester Activities on the Final Grade | 1 | 60 |
| Total |
| Semester Activities | Number | Duration (Hours) | Workload |
|---|---|---|---|
| Course Hours (Including exam week: 16 x total hours) | 16 | 3 | 48 |
| Laboratory / Application Hours (Including exam week: 16 x total hours) | 16 | ||
| Study Hours Out of Class | 14 | 5 | 70 |
| Field Work | |||
| Quizzes / Studio Critiques | - | - | |
| Portfolio | |||
| Homework / Assignments | - | - | |
| Presentation / Jury | |||
| Project | |||
| Seminar / Workshop | |||
| Oral Exam | |||
| Midterms | 1 | 42 | |
| Final Exams | 1 | 50 | |
| Total | 210 |
| # | Program Competencies/Outcomes | * Contribution Level | ||||
1 | 2 | 3 | 4 | 5 | ||
| 1 | To be able to have a grasp of basic mathematics, applied mathematics or theories and applications of statistics. | X | ||||
| 2 | To be able to use advanced theoretical and applied knowledge, interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the fields of mathematics or statistics. | |||||
| 3 | To be able to apply mathematics or statistics in real life phenomena with interdisciplinary approach and discover their potentials. | X | ||||
| 4 | To be able to evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach and develop positive attitude towards lifelong learning. | X | ||||
| 5 | To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals. | X | ||||
| 6 | To be able to take responsibility both as a team member or individual in order to solve unexpected complex problems faced within the implementations in the field, planning and managing activities towards the development of subordinates in the framework of a project. | |||||
| 7 | To be able to use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge. | |||||
| 8 | To be able to act in accordance with social, scientific, cultural and ethical values on the stages of gathering, implementation and release of the results of data related to the field. | |||||
| 9 | To be able to possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also environmental protection, worker's health and security. | |||||
| 10 | To be able to connect concrete events and transfer solutions, collect data, analyze and interpret results using scientific methods and having a way of abstract thinking. | |||||
| 11 | To be able to collect data in the areas of Mathematics or Statistics and communicate with colleagues in a foreign language. | |||||
| 12 | To be able to speak a second foreign language at a medium level of fluency efficiently. | |||||
| 13 | To be able to relate the knowledge accumulated throughout the human history to their field of expertise. | |||||
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest
