Syllabus ( MATH 582 )
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Basic information
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| Course title: |
Probability And Mathematical Statistics II |
| Course code: |
MATH 582 |
| Lecturer: |
Prof. Dr. Nuri ÇELİK
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| ECTS credits: |
7.5 |
| GTU credits: |
3 (3+0+0) |
| Year, Semester: |
1/2, Fall and Spring |
| Level of course: |
Second Cycle (Master's) |
| Type of course: |
Area Elective
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| Language of instruction: |
English
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| Mode of delivery: |
Face to face , Group study
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| Pre- and co-requisites: |
None |
| Professional practice: |
No |
| Purpose of the course: |
The main objective of this course is to teach students advanced topics in probability and mathematical statistics and to prepare them for conducting research, particularly in asymptotic theory. |
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Learning outcomes
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Upon successful completion of this course, students will be able to:
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construct a solid background and understanding of the basic results and methods in advanced probability theory and mathematical statistics.
Contribution to Program Outcomes
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Define and manipulate advanced concepts of Mathematics
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Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
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Develop mathematical, communicative, problem-solving, brainstorming skills.
Method of assessment
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Written exam
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Homework assignment
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perceive the weak convergency, convergency with respect to measure and distribution.
Contribution to Program Outcomes
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Define and manipulate advanced concepts of Mathematics
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Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
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Develop mathematical, communicative, problem-solving, brainstorming skills.
Method of assessment
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Written exam
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apply the methods for obtaining asymptotic distribution of estimation and tests statistics for the relal life problems.
Contribution to Program Outcomes
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Define and manipulate advanced concepts of Mathematics
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Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
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Develop mathematical, communicative, problem-solving, brainstorming skills.
Method of assessment
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Written exam
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Homework assignment
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Contents
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| Week 1: |
Convergency of Distributions; Weak convergency, |
| Week 2: |
Characteristic functions; inversion and the Uniqness theorem. |
| Week 3: |
Centeral limit theorem; Lindeberg and Lyapounov Theorems, Feller's theorem, Limit theorem in R^k. |
| Week 4: |
Large sample behavior of emprical distributions and order statistics. |
| Week 5: |
Asymptotic behavior of Estimators; Asymptotic behavior of Maximum likelihood estimators, Asymptotic behavior of U-statistics and related estimators. Asymptotic efficiency of estimators.
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| Week 6: |
Optimal Test; Randomized test, Strong testler, Neymann-Pearson Lemma. |
| Week 7: |
Asymptotic behavior of Test statistics
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| Week 8: |
Conditional Probability; Additive set function, Hann Decomposition, Absolute continuity and Singularity. |
| Week 9: |
Radon-Nikodym Theorem. Midterm Exam. |
| Week 10: |
Conditional Probability; Properties of conditional probability, Conditional probability distribution. |
| Week 11: |
Conditional expectations |
| Week 12: |
Martingales; submartingales, function of martingales. |
| Week 13: |
Martingale convergence theorems, Applications to Likelihood ratio test, Bayes Estimation. |
| Week 14: |
Kolmogorov's existance theorem-finite dimensional distribıtions |
| Week 15*: |
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| Week 16*: |
Final Exam. |
| Textbooks and materials: |
Probability and measure by Patrick Bilingsley
Statistical Inference, by Casella and Berger,
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| Recommended readings: |
Arnold, S. F. Mathematical Statistics, Prentice HallI
Introduction to Mathematical Statistics by Hogg and Craig
Introduction to Probability Models by Ross
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* Between 15th and 16th weeks is there a free week for students to prepare for final exam.
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Assessment
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| Method of assessment |
Week number |
Weight (%) |
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| Mid-terms: |
9 |
40 |
| Other in-term studies: |
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0 |
| Project: |
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0 |
| Homework: |
1,2,3,4,5 |
10 |
| Quiz: |
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0 |
| Final exam: |
16 |
50 |
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Total weight: |
(%) |
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Workload
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| Activity |
Duration (Hours per week) |
Total number of weeks |
Total hours in term |
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| Courses (Face-to-face teaching): |
3 |
14 |
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| Own studies outside class: |
4 |
14 |
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| Practice, Recitation: |
0 |
0 |
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| Homework: |
10 |
5 |
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| Term project: |
0 |
0 |
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| Term project presentation: |
0 |
0 |
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| Quiz: |
0 |
0 |
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| Own study for mid-term exam: |
15 |
1 |
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| Mid-term: |
1 |
1 |
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| Personal studies for final exam: |
20 |
1 |
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| Final exam: |
2 |
1 |
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Total workload: |
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Total ECTS credits: |
* |
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* ECTS credit is calculated by dividing total workload by 25.
(1 ECTS = 25 work hours)
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