TR
11111

COURSE INTRODUCTION AND APPLICATION INFORMATION

dm.ieu.edu.tr

Course Name
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
Spring
Prerequisites
None
Course Language
Course Type
Required
Course Level
-
Mode of Delivery -
Teaching Methods and Techniques of the Course
Course Coordinator -
Course Lecturer(s)
Assistant(s) -
Course Objectives
Learning Outcomes The students who succeeded in this course;
  • will be able to get a deep knowledge on the basics of statistics and mathematics.
  • will be able to propose and evaluate tests.
  • will be able to find confidence intervals.
  • will be able to find moment estimators and maximum likelihood estimators.
  • will be able to work with order statistics and find and apply the sufficient statistic.
Course Description

 



Course Category

 Core Courses
X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Required Materials
1 Introduction to basic concepts of statistics. Sampling from infinite population, simple random sample, stratified sample, cluster sampling, systematic sample. “Statistical Inference” by G. Casella, R. L. Berger, Duxbury Press, California: 201:210.
2 Preliminary material: Convergence of sequences of random variables, types of convergence. The moment generation function. The law of large numbers, the central limit theorem. “Statistical Inference” by G. Casella, R. L. Berger, Duxbury Press, California: 213:228.
3 Parametric and nonparametric statistics, examples. Empirical distribution function. Glivenko-Cantelli theorem. “Mathematical Statistics” by A. A. Borovkov, Gordon and Breach Science Publishers: 1:7
4 Order statistics. “Statistical Inference” by G. Casella, R. L. Berger, Duxbury Press, California: 228:237
5 Sample characteristics. Main types of statistics. “Mathematical Statistics” by A. A. Borovkov, Gordon and Breach Science Publishers: 7:12
6 Continuity theorems. Limit distributions of statistics of type I and type II. “Mathematical Statistics” by A. A. Borovkov, Gordon and Breach Science Publishers: 13:35
7 Estimation of unknown parameters. Properties of estimators. Some parametric families of distributions. “Mathematical Statistics” by A. A. Borovkov, Gordon and Breach Science Publishers: 40:50
8 The main method for obtaining estimators. Realization of substitutional method in the parametric case. “Mathematical Statistics” by A. A. Borovkov, Gordon and Breach Science Publishers: 51:66
9 Midterm exam
10 Consistency and asymptotic normality of estimators. The method of moments. M- estimators. Consistency of M-estimators. “Mathematical Statistics” by A. A. Borovkov, Gordon and Breach Science Publishers: 51:66
11 Method of minimal distance. The maximum likelihood method. “Mathematical Statistics” by A. A. Borovkov, Gordon and Breach Science Publishers: 65:80
12 Data reduction and the sufficiency principle. “Statistical Inference” by G. Casella, R. L. Berger, Duxbury Press, California: 246:258
13 Complete statistics. The likelihood and invariance principle. “Statistical Inference” by G. Casella, R. L. Berger, Duxbury Press, California: 259:275
14 Hypothesis testing. Methods of finding tests. The Neiman-Pearson Lemma. Most powerful tests. “Statistical Inference” by G. Casella, R. L. Berger, Duxbury Press, California: 345:403
15 Interval estimation. “Statistical Inference” by G. Casella, R. L. Berger, Duxbury Press, California: 403:461
16 Linear regression, the analysis of variance. “Statistical Inference” by G. Casella, R. L. Berger, Duxbury Press, California: 509:554
Course Notes/Textbooks “Statistical Inference” by G. Casella, R. L. Berger, Duxbury Press, “Mathematical statistics” by A. A. Borovkov, Gordon and Breach Science Publishers
Suggested Readings/Materials “Mathematical Statistics” by J. Shao, Springer.

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
2
20
Portfolio
Homework / Assignments
1
10
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterm
1
30
Final Exam
1
40
Total

Weighting of Semester Activities on the Final Grade
4
60
Weighting of End-of-Semester Activities on the Final Grade
1
40
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Course Hours
(Including exam week: 16 x total hours)
16
3
48
Laboratory / Application Hours
(Including exam week: 16 x total hours)
16
Study Hours Out of Class
15
3
Field Work
Quizzes / Studio Critiques
2
1
Portfolio
Homework / Assignments
1
10
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterms
1
20
Final Exams
1
33
    Total
158

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
 Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1 To have a grasp of basic mathematics, applied mathematics and theories and applications of statistics. X
2 To be able to use theoretical and applied knowledge acquired in the advanced fields of mathematics and statistics, X
3 To be able to define and analyze problems and to find solutions based on scientific methods, X
4 To be able to apply mathematics and statistics in real life with interdisciplinary approach and to discover their potentials, X
5 To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, X
6 To be able to criticize and renew her/his own models and solutions, X
7 To be able to tell theoretical and technical information easily to both experts in detail and nonexperts in basic and comprehensible way, X
8

To be able to use international resources in English and in a second foreign language from the European Language Portfolio (at the level of B1) effectively and to keep knowledge up-to-date, to communicate comfortably with colleagues from Turkey and other countries, to follow periodic literature,

 X
9

To be familiar with computer programs used in the fields of mathematics and statistics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level,
10

To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement,
11 To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense,
12

By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere,

 X
13

To be able to continue lifelong learning by renewing the knowledge, the abilities and the compentencies which have been developed during the program, and being conscious about lifelong learning,
14

To be able to adapt and transfer the knowledge gained in the areas of mathematics and statistics to the level of secondary school,
15

To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively.

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

 

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