Mathematical Statistics II
renginnar@gmail.com
Content
Objective
The course is an introduction to the theoretical foundations of modeling and estimation methods used in many statistical applications. It provides essential mathematical perspective and tools and underlines the role of mathematics in applied statistics.
Course Content
Introduction: Modelisation of random events
Part I: Special probability distributions
Discrete distributions (uniform, bernoulli, binomial, geometric, hypergoemetric,
negative binomial, poisson)
Continuous distributions (uniform, exponential, gamma, chi-square, beta, normal)
Part II: Moments
Central and non-central moments
Moment generating functions
Part III: Estimation and inference
Sampling, Law of Large Numbers and Central Limit Theorem
Point estimation (method of moments and maximum likelihood estimation)
Sampling distribution of estimators
Con fidence intervals
Hypothesis testing
Part IV:Simple linear regression
Ordinary least square estimation of parameters
Course Learning Outcomes
Students have basic perspectives on how to approach the modeling of a random event through special probability distributions and the role of their parameters. They can use properties of moments and moment-generating functions to obtain various population statistics.
They understand conditions for limiting distributions, convergence and the critical role of CLT.
They can obtain method of moments and maximum likelihood estimators of population
mean, proportion, and variance. They understand the sampling distribution of an estimator and
use it for hypothesis testing. They can derive interval estimates of parameters. They know
the principle of least squares and solve for estimators of parameters of simple linear regression
model.
Teaching and Learning Methods
This course is a prerequisite for ECON305 Econometrics.
ECON207 Mathematical Statistics I is a prerequisite for this course.
Good grasp of multivariate calculus and basic linear algebra are necessary minimum to follow the content.
References
1.Schay, G. (2007), Introduction to Probability with Statistical Application, Birkhauser
Boston.
2. Sheldon, Ross (2004), Introduction to Probability and Statistics for Engineers and
Scientists, Third Edition, Elsevier Academic Press.
3. Fourastie J. et Laslier J.F (1987), Probabilites et Statistiques, Dunod-Paris.
4. Grais, B. (1994), Methodes Statistiques: Tome 2, Dunod, Paris.
Assessment System
| Activities | Number | Contribution |
|---|---|---|
| Contribution of in-term studies to overall grade | 1 | 40 |
| Contribution of final exam to overall grade | 1 | 60 |
| Total | 2 | 100 |
| Activities | Number | Contribution |
|---|---|---|
| Assignments | 0 | 0 |
| Presentation | 0 | 0 |
| Midterm Examinations (including preparation) | 1 | 40 |
| Project | 0 | 0 |
| Laboratory | 0 | 0 |
| Other Applications | 0 | 0 |
| Quiz | 0 | 0 |
| Term Paper/ Project | 0 | 0 |
| Portfolio Study | 0 | 0 |
| Reports | 0 | 0 |
| Learning Diary | 0 | 0 |
| Thesis/ Project | 0 | 0 |
| Seminar | 0 | 0 |
| Other | 0 | 0 |
| Total | 1 | 40 |
Relation of Proficiency
| No | Program Learning Outcomes | Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Demonstrate a basic knowledge of different economic theories and main discussions driving current theoretical approaches | |||||
| 2 | Demonstrate ability to use basic qualitative and quantitative methods to asses different economic questions of applied fields | |||||
| 3 | Show a sound understanding of current economic discussions and problems | |||||
| 4 | Have an effective and clear communication in written and oral formats in different public and professional contexts. | |||||
| 5 | Demonstrate basic knowledge of the world economic history and a sound knowledge of the Turkish economic history | |||||
| 7 | Demonstrate knowledge of standard quantitative techniques and empirical models used in economics | |||||
| 8 | Show ability to apply basic economic theory to an applied topic | |||||
| 9 | Show a basic understanding of analytical methods, both theory- and model-based | |||||
| 10 | Show ability to use economic concepts to discuss current economic issues | |||||
| 11 | Reason logically and work analytically | |||||
| 12 | Show awareness on social aspects of the economics in different applied and theoretical fields | |||||
| 13 | Identify appropriate economic models to analyse problems | |||||
| 16 | Show understanding of basic statistical and econometric concepts and ability to apply basic concepts to own empirical work | |||||
| 17 | Demonstrate a sound knowledge of the current economic issues in Turkey and a general knowledge of the issues in the world economy | |||||
ECTS
| Activities | Number | Period | Total Workload |
|---|---|---|---|
| Class Hours | 14 | 4 | 56 |
| Working Hours out of Class | 14 | 3 | 42 |
| Midterm Examinations (including preparation) | 1 | 11 | 11 |
| Final Examinations (including preparation) | 1 | 16 | 16 |
| Total Workload | 125 | ||
| Total Workload / 25 | 5.00 | ||
| Credits ECTS | 5 | ||