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Information
| Code | IEM1824 |
| Name | Estimation Theory |
| Term | 2022-2023 Academic Year |
| Term | Spring |
| Duration (T+A) | 4-0 (T-A) (17 Week) |
| ECTS | 8 ECTS |
| National Credit | 4 National Credit |
| Teaching Language | Türkçe |
| Level | Doktora Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. GÜLSEN KIRAL |
| Course Instructor |
1 |
Course Goal / Objective
The aim of this course is to provide students an infrastructure about basic concepts and algorithms of estimation theory to be used in their research and statistical applications.
Course Content
This lesson covers estimators, properties of estimators, methods for the estimation of the parameters, minimum variance estimation, maximum likelihood and method of moments, estimation of the random parameters,the smallest average root mean square error estimators and maximum a posteriori, least squares and Kalman filter approach by using sequential and recursive estimation, Monte-Carlo methods.
Course Precondition
There are no prerequisites.
Resources
A. Papoulis, Probability, Random Variables and Stochastic Processes, 4th ed., McGraw Hill, 2002
Notes
Source books, statistical packages
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | It underlines the basic estimation methodologies such as Minimum variance unbiased estimator, Maximum likelihood estimator, Moment method estimator. |
| LO02 | Evaluate the estimators by using bias, efficiency, and consistency. |
| LO03 | Evaluates the main differences between classical and Bayesian estimation methods. |
| LO04 | Evaluates the calculation methods of the upper bounds of the estimators. |
| LO05 | Interpret basic estimation methodologies by applying real statistical problems. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Identify an econometric problem and propose a new solution to it | 2 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Develops new knowledge using current concepts in Econometrics, Statistics and Operations Research | 2 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Explain for what purpose and how econometric methods are applied to other fields and disciplines | 3 |
| PLO04 | Beceriler - Bilişsel, Uygulamalı | Using her knowledge, brings original solutions to problems in Economics, Business Administration and other social sciences | 2 |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | Creates a new model using mathematics, statistics and econometrics knowledge to solve the problem encountered | 3 |
| PLO06 | Beceriler - Bilişsel, Uygulamalı | Interprets the results obtained from the most appropriate method to predict the model | 4 |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Performs conceptual analysis to develop solutions to problems | 4 |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Collects data on purpose | |
| PLO09 | Beceriler - Bilişsel, Uygulamalı | Synthesizes the information obtained by using different sources within the framework of academic rules in a field that does not research | 3 |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | Presents analysis results conveniently | 4 |
| PLO11 | Beceriler - Bilişsel, Uygulamalı | Converts its findings into a master's thesis or a professional report in Turkish or a foreign language | 2 |
| PLO12 | Beceriler - Bilişsel, Uygulamalı | It researches current approaches and methods to solve the problems it encounters and proposes new solutions | 2 |
| PLO13 | Beceriler - Bilişsel, Uygulamalı | Develops long-term plans and strategies using econometric and statistical methods | 2 |
| PLO14 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Performs self-study using knowledge of Econometrics, Statistics and Operations to solve a problem | 3 |
| PLO15 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Leads the team by taking responsibility | |
| PLO16 | Yetkinlikler - Öğrenme Yetkinliği | Being aware of the necessity of lifelong learning, it constantly renews itself by following the current developments in the field of study | 4 |
| PLO17 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Uses acquired knowledge in the field to determine the vision, aim, and goals for an organization/institution | |
| PLO18 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Uses a package program of Econometrics, Statistics, and Operation Research or writes a new code | 2 |
| PLO19 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Interprets the feelings, thoughts and behaviors of the related persons correctly/expresses himself/herself correctly in written and verbal form | 3 |
| PLO20 | Yetkinlikler - Alana Özgü Yetkinlik | Applies social, scientific and professional ethical values | 3 |
| PLO21 | Yetkinlikler - Alana Özgü Yetkinlik | Interprets data on economic and social events by following current issues | 2 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Introduction to estimation theory, mathematical formulation of the estimation problem, Estimation performance evaluation. | Examining the relevant chapter in the book. | Öğretim Yöntemleri: Anlatım |
| 2 | Unbiased estimators, minimum variance criterion, the minimum variance unbiased (MVUE) estimator. | Examining the relevant chapter in the book. | Öğretim Yöntemleri: Anlatım |
| 3 | The Cramer-Rao lower bound (CRLB) | Examining the relevant chapter in the book. | Öğretim Yöntemleri: Anlatım |
| 4 | The expression of CRBL for Gaussian Distribution, linear model, linear model examples | Examining the relevant chapter in the book. | Öğretim Yöntemleri: Anlatım |
| 5 | The general MVUE, sufficient statistics, calculation of MVUE with sufficient statistics | Examining the relevant chapter in the book. | Öğretim Yöntemleri: Anlatım |
| 6 | The best linear predictor (BLUE), definition and calculation of BLUE | Examining the relevant chapter in the book. | Öğretim Yöntemleri: Anlatım |
| 7 | Maximum likelihood estimation (MLE), MLE calculation, asymptotic properties of MLE | Examining the relevant chapter in the book. | Öğretim Yöntemleri: Anlatım |
| 8 | Mid-Term Exam | Examining the relevant chapter in the book. | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Numerical calculation of MLE , the MLE for the vector parameters | Examining the relevant chapter in the book. | Öğretim Yöntemleri: Anlatım |
| 10 | Smallest quadratic estimation, the smallest linear quadratic estimation, constrained estimation of the smallest quadratic | Examining the relevant chapter in the book. | Öğretim Yöntemleri: Anlatım |
| 11 | Method of Moment estimation, introduction to Bayesian estimation | Examining the relevant chapter in the book. | Öğretim Yöntemleri: Anlatım |
| 12 | The philosophy of Bayesian estimation, the usege of prior knowledge of the parameter | Examining the relevant chapter in the book. | Öğretim Yöntemleri: Anlatım |
| 13 | Bayesian linear model, unwanted parameters (nuisance parameters), general Bayesian estimation. | Examining the relevant chapter in the book. | Öğretim Yöntemleri: Anlatım |
| 14 | Minimum mean square error estimation | Examining the relevant chapter in the book. | Öğretim Yöntemleri: Anlatım |
| 15 | Linear Bayesian estimation, linear minimum mean square error estimation | Examining the relevant chapter in the book. | Öğretim Yöntemleri: Anlatım |
| 16 | Term Exams | Examining the relevant chapter in the book. | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Examining the relevant chapter in the book. | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 4 | 56 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 8 | 112 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 2 | 4 | 8 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 24 | 24 |
| Total Workload (Hour) | 212 | ||
| Total Workload / 25 (h) | 8,48 | ||
| ECTS | 8 ECTS | ||