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| IST2008 | Mathematical Statistics | 4+0+0 | ECTS:6 | | Year / Semester | Spring Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of STATISTICS and COMPUTER SCIENCES | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Prof. Dr. Zafer KÜÇÜK | | Co-Lecturer | None | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | To understand basic mathematical statistical concepts, to criticize and to make the relationship between the theory and applications. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | understand the parameter estimation and hypothesis testing | 1,2,5,8 | 1, | | LO - 2 : | infer the statistical results about the parameter estimation | 1,2,5,8 | 1, | | LO - 3 : | make mathematical comments for statistical results | 1,2,5,8 | 1, | | LO - 4 : | make statistical inferences about parameter with hypothesis tests | 1,2,5,8 | 1, | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome | | |
| Sampling, distributions, prediction, hypothesis test, Chi-square test, simple regression and correlation, simple analysis of variance, time series analysis, index number. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Basic concepts, background information, mass, parameters and sampling concepts. Distribution of sample statistics | | | Week 2 | Asymptotic properties of estimators, convergence in probability (law of large numbers), convergence in distribution (central limit theorem), moment convergence in | | | Week 3 | Order statistics and associated some statistics (mode, median, percentile, etc.) | | | Week 4 | Introduction to estimation of parameter | | | Week 5 | Properties required in estimators; neutrality, competence | | | Week 6 | Consistency, efficiency, completeness, the best neutral estimators, Cramer-Rao inequality | | | Week 7 | Review and problem solution | | | Week 8 | Mid-term exam | | | Week 9 | Rao-Blackwell theorem, Lehmann-Scheffe theorem of uniqueness | | | Week 10 | Distribution properties of estimators (with the help of Taylor series acquisition of the asymptotic distribution and some features) | | | Week 11 | An introduction to hypothesis testing problem; parameters, hypothesis, simple and complex hypotheses, test function | | | Week 12 | Error probabilities and power functions, the most powerful tests | | | Week 13 | Likelihood ratio tests and Neymann-Pearson Lemma | | | Week 14 | Applications of Neymann-Pearson lemma, complex hypothesis testing | | | Week 15 | Karlin-Rubin theorem and hypothesis testing applications, review and problem solving | | | Week 16 | End-of-term exam | | | |
| 1 | Öztürk, F. (1993). Matematiksel İstatistik; olasılık uzayları ve rastgele değişkenler . AÜFF Döner Sermaye, Ankara. | | | |
| 1 | Hogg, Robert, V., Craig, Allan, T. (1978). Introduction to Mathematical Statistics. 4 nd ed., New York: Macmillan. | | | 2 | Casella, G. (2001). Statistical Inference. Pacific Grove, Calif. : Wadsworth. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 09/04/2019 | 2 | 50 | | End-of-term exam | 9 | 29/05/2019 | 2 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 4 | 14 | 56 | | Sınıf dışı çalışma | 5 | 14 | 70 | | Laboratuar çalışması | 0 | 0 | 0 | | Arasınav için hazırlık | 10 | 1 | 10 | | Arasınav | 0 | 1 | 0 | | Uygulama | 0 | 0 | 0 | | Klinik Uygulama | 0 | 0 | 0 | | Ödev | 5 | 4 | 20 | | Proje | 0 | 0 | 0 | | Kısa sınav | 3 | 1 | 3 | | Dönem sonu sınavı için hazırlık | 15 | 1 | 15 | | Dönem sonu sınavı | 2 | 1 | 2 | | Diğer 1 | 0 | 0 | 0 | | Diğer 2 | 0 | 0 | 0 | | Total work load | | | 176 |
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