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Information
| Code | ISB538 |
| Name | Theory of Statistics |
| Term | 2024-2025 Academic Year |
| Term | Spring |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Yüksek Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. GÜLESEN ÜSTÜNDAĞ ŞİRAY |
| Course Instructor |
1 |
Course Goal / Objective
The goal are to gain the necessary information for statistical applications by understanding the basic theory of statistics.
Course Content
The content of this course is limiting distributions, statistical inference, sufficient statistics.
Course Precondition
To have learned the lecture ISB 537 Theory of Probability
Resources
1. Robert V. Hogg. Allen T. Craig. Introduction to Mathematical. Statistics. Fifth Edition. Macmillan Publishing Co. Inc. New York. 2. George Casella, Roger L. Berger. Statistical Inference. Duxbury Press. 3. Yılmaz Akdi. Matematiksel İstatistiğe Giriş. Gazi Kitabevi.
Notes
Lecture Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Explain convergency in distribution, probability and moments. |
| LO02 | Find the distributions of sample statistics. |
| LO03 | Make the statistical inference. |
| LO04 | Explain the methods of point estimation. |
| LO05 | Compare the estimator by means of the measures of quality. |
| LO06 | Obtain the sufficient statistics. |
| LO07 | Explain the completeness, uniqueness and consistency. |
| LO08 | Obtain the exponential class of probabilty density functions. |
| LO09 | Explain the minimal sufficient and ancillary statistics. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Have in-depth theoretical and practical knowledge about Probability and Statistics | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | They have the knowledge to make doctoral plans in the field of statistics. | 4 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Has comprehensive knowledge about analysis and modeling methods used in statistics. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Has comprehensive knowledge of methods used in statistics. | 4 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Make scientific research on Mathematics, Probability and Statistics. | |
| PLO06 | Bilgi - Kuramsal, Olgusal | Indicates statistical problems, develops methods to solve. | 4 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Apply innovative methods to analyze statistical problems. | |
| PLO08 | Bilgi - Kuramsal, Olgusal | Designs and applies the problems faced in the field of analytical modeling and experimental researches. | |
| PLO09 | Bilgi - Kuramsal, Olgusal | Access to information and do research about the source. | 4 |
| PLO10 | Bilgi - Kuramsal, Olgusal | Develops solution approaches in complex situations and takes responsibility. | |
| PLO11 | Bilgi - Kuramsal, Olgusal | Has the confidence to take responsibility. | |
| PLO12 | Beceriler - Bilişsel, Uygulamalı | They demonstrate being aware of the new and developing practices. | |
| PLO13 | Beceriler - Bilişsel, Uygulamalı | He/She constantly renews himself/herself in statistics and related fields. | |
| PLO14 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Communicate in Turkish and English verbally and in writing. | |
| PLO15 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Transmits the processes and results of their studies clearly in written and oral form in national and international environments. | |
| PLO16 | Yetkinlikler - Öğrenme Yetkinliği | It considers the social, scientific and ethical values in the collection, processing, use, interpretation and announcement stages of data and in all professional activities. | |
| PLO17 | Yetkinlikler - Öğrenme Yetkinliği | Uses the hardware and software required for statistical applications. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Convergency in distribution and in probability | Reading the related references and solving problem | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 2 | Limiting moment generating function | Reading the related references and solving problem | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Problem Çözme |
| 3 | The central limit theorem and some theorems on limiting distributions | Reading the related references and solving problem | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Problem Çözme |
| 4 | Point estimation, confidence intervals | Reading the related references and solving problem | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Problem Çözme, Alıştırma ve Uygulama |
| 5 | Tests of statistical hypothesis | Reading the related references and solving problem | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Problem Çözme |
| 6 | Additional comments about statistical tests | Reading the related references and solving problem | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Problem Çözme, Alıştırma ve Uygulama |
| 7 | Measures of quality of estimators | Reading the related references and solving problem | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Problem Çözme, Alıştırma ve Uygulama |
| 8 | Mid-Term Exam | Review the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Suffient statistics | Reading the related references and solving problem | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Problem Çözme |
| 10 | Properties of a sufficient statistics | Reading the related references and solving problem | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Problem Çözme |
| 11 | Completeness and uniqueness | Reading the related references and solving problem | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Problem Çözme |
| 12 | The exponential class of probability density functions | Reading the related references and solving problem | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Problem Çözme, Alıştırma ve Uygulama |
| 13 | Functions of a parameter | Reading the related references and solving problem | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Problem Çözme |
| 14 | The case of several parameter | Reading the related references and solving problem | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Problem Çözme |
| 15 | Minimal sufficient and ancillary statistics | Reading the related references and solving problem | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Problem Çözme |
| 16 | Term Exams | Review the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Review the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 5 | 70 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 15 | 15 |
| Final Exam | 1 | 30 | 30 |
| Total Workload (Hour) | 157 | ||
| Total Workload / 25 (h) | 6,28 | ||
| ECTS | 6 ECTS | ||