DEGREE PROGRAMS  Associate's Degree (Short Cycle)  Bachelor’s Degree (First Cycle)  Master’s Degree (Second Cycle)

Course Description Course Name : Theory of Statistics Course Code : ISB-538 Course Type : Compulsory Level of Course : Second Cycle Year of Study : 1 Course Semester : Spring (16 Weeks) ECTS : 6 Name of Lecturer(s) : Asst.Prof.Dr. GÜLESEN ÜSTÜNDAĞ ŞİRAY Learning Outcomes of the Course : Explain convergency in distribution and in probability. Explain the limiting distributions and properties of them. Make statistical inference. Explain and obtain the measures of quality of estimators. Explain and obtain sufficient statistics. Explain and use the completeness, uniqueness and consistency. Obtain the exponential class of probabilty density functions. Explain the minimal sufficient and ancillary statistics. Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : This course aims to provide information on principal statistical theory and its applications. Course Contents : Limiting distributions, Introduction to statistical inference, Sufficient statistics Language of Instruction : Turkish Work Place : Seminar room of the department   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Convergency in distribution and in probability Reading the related references Lecture, discussion, problem-solving 2 Limiting moment generating function Reading the related references Lecture, discussion, problem-solving 3 The central limit theorem and some theorems on limiting distributions Reading the related references Lecture, discussion, problem-solving 4 Point estimation, confidence intervals Reading the related references Lecture, discussion, problem-solving 5 Tests of statistical hupothesis Reading the related references Lecture, discussion, problem-solving 6 Additional comments about statistical tests Reading the related references Lecture, discussion, problem-solving 7 Measures of quality of estimators Reading the related references Lecture, discussion, problem-solving 8 Mid-term Exam Review the topics discussed in the lecture notes and sources Written exam 9 Suffient statistics Reading the related references Lecture, discussion, problem-solving 10 Properties of a sufficient statistics Reading the related references Lecture, discussion, problem-solving 11 Completeness and uniqueness Reading the related references Lecture, discussion, problem-solving 12 The exponential class of probability density functions Reading the related references Lecture, discussion, problem-solving 13 Functions of a parameter Reading the related references Lecture, discussion, problem-solving 14 The case of several parameters Reading the related references Lecture, discussion, problem-solving 15 Minimal sufficient and ancillary statistics Reading the related references Lecture, discussion, problem-solving 16/17 Final Exam Review the topics discussed in the lecture notes and sources Written exam   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  Hogg,R.V. And Craig, A.T. (2005). Introduction to Mathematical Statistics. Prentice Hall, Sixth Edition.  Akdi, Y. (2010). Matematiksel İstatistiğe Giriş , Gazi Kitabevi, ANKARA.  Casella, G. and Berger, R.L. (2002). Statistical Inference. Duxbury, Second Edition. Required Course Material(s)   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 1 60     Homeworks/Projects/Others 5 40 Total 100 Rate of Semester/Year Assessments to Success 40   Final Assessments 100 Rate of Final Assessments to Success 60 Total 100   Contribution of the Course to Key Learning Outcomes # Key Learning Outcome Contribution* 1 Possess advanced level of theoretical and applicable knowledge in the field of Probability and Statistics. 5 2 Conduct scientific research on Mathematics, Probability and Statistics. 4 3 Possess information, skills and competencies necessary to pursue a PhD degree in the field of Statistics. 4 4 Possess comprehensive information on the analysis and modeling methods used in Statistics. 3 5 Present the methods used in analysis and modeling in the field of Statistics. 2 6 Discuss the problems in the field of Statistics. 4 7 Implement innovative methods for resolving problems in the field of Statistics. 5 8 Develop analytical modeling and experimental research designs to implement solutions. 3 9 Gather data in order to complete a research. 3 10 Develop approaches for solving complex problems by taking responsibility. 4 11 Take responsibility with self-confidence. 2 12 Have the awareness of new and emerging applications in the profession 3 13 Present the results of their studies at national and international environments clearly in oral or written form. 0 14 Oversee the scientific and ethical values during data collection, analysis, interpretation and announcment of the findings. 0 15 Update his/her knowledge and skills in statistics and related fields continously 0 16 Communicate effectively in oral and written form both in Turkish and English. 0 17 Use hardware and software required for statistical applications. 0 * Contribution levels are between 0 (not) and 5 (maximum).   Student Workload - ECTS Works Number Time (Hour) Total Workload (Hour) Course Related Works     Class Time (Exam weeks are excluded) 14 3 42     Out of Class Study (Preliminary Work, Practice) 14 3 42 Assesment Related Works     Homeworks, Projects, Others 5 8 40     Mid-term Exams (Written, Oral, etc.) 1 10 10     Final Exam 1 15 15 Total Workload: 149 Total Workload / 25 (h): 5.96 ECTS Credit: 6