Download 0236126

Title
Introduction to The Theory of
Statistics.
Code
Local
Credit
ECTS
Lecture
(hour/week)
Practical
(hour/week)
Laboratory
(hour/week)
0236126
3
7.5
3
0
0
Prerequisite
None
Semester
Not set
Course Language
Not set
Level Of Course
Third Cycle
Course Type
Elective @ Statistics Division - Statistics PhD. Program
Course Category
Major Area Courses
Mode Of Delivery
Face-to-Face
Owner Academic Unit
Statistics
Course Coordinator
Atıf Evren
Instructor(s)
Asistant(s)
Course Objectives
Fundamentals of statistical theory
Course Content
Probability, random variables,expectations,limit theorems,some parametric
families,sampling and reduction of data,estimation, testing hypotheses.
Recommended Or
Required Reading




Recommended Optional
Program Components
- Lecture notes.
- MOOD, A.M. vd (1974) Introduction to the Theory of Statistics, McGrawHill International Editions, (3rd edition)
- LINDGREN, B.W., Statistical Theory, Chapman&Hall, 4th edition
- SHAO, J., Mathematical Statistics, Springer
None
Course Learning Outcomes
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Essentials of probability theory.
Multivariate distributions.
Functions of random variables.
Sampling distributions.
Statistical estimation.
Properties of estimators.
Bayes estimators.
Methods for finding confidence intervals.
Hypothesis tests.
Generalized likelihood ratio test.
Weekly Subjects and Related Preparation Studies
Week
1
2
3
4
5
Subjects
Probability. Random variables. Probability functions.
Distribution functions and expectation.
Moments and moment generating functions. Special
parametric families of univariate distributions.
Joint and conditional distributions. Stochastic
independence.
Expectation. Covariance and correlation coefficient.
Cauchy-Schwarz Inequality.
Bivariate normal distribution. Distributions of functions
Related Preparation
Mood, Graybill, Boes, Chapter I
Mood, Graybill, Boes, Chapter II-III
Mood, Graybill, Boes, Chapter IV
Mood, Graybill, Boes, Chapter IV
Mood, Graybill, Boes, Chapter IV-V
6
7
8
9
10
11
12
13
14
15
16
of random variables.
Cumulative-distribution-function technique. Momentgenerating-function technique. Transformations.
Sampling and sampling distributions. Sampling from the
normal distribution.
Midterm examination.
Parametric point estimation. Methods for finding
estimators. Method of moments. Maximum likelihood.
Other methods.
Properties of point estimators. Sufficiency. Unbiased
estimation. Lower bound for variance. Sufficiency and
completeness. Location or scale invariance.
Bayes estimators. Posterior distribution. Loss-function
approach. Minimax estimator.
Parametric interval estimation. Confidence intervals.
Sampling from the normal distribution.Methods of
finding confidence intervals.
Hypothesis tests. Generalized likelihood-ratio test.
Uniformly most powerful tests. Unbiased tests. Methods
of finding tests.
Sampling from the normal distribution.
Chi-square tests. Asymptotic distribution of generalized
likelihood ratio. Chi-square goodness of fit test. Test of
the equality of two multinomial distributions. Tests of
independence in contingency tables.
Final examination.
Mood, Graybill, Boes, Chapter V
Mood, Graybill, Boes, Chapter VI
General review
Mood, Graybill, Boes, Chapter VII
Mood, Graybill, Boes, Chapter VII
Mood, Graybill, Boes, Chapter VII
Mood, Graybill, Boes, Chapter VIII
Mood, Graybill, Boes, Chapter IX
Mood, Graybill, Boes, Chapter IX
Mood, Graybill, Boes, Chapter IX
General review
Evaluation System
Activities
Number
Attendance/Participation
Laboratory
Application
Field Work
Special Course Internship (Work Placement)
Quizzes/Studio Critics
Homework Assignments
2
Presentations/Jury
Project
Seminar/Workshop
Mid-Terms
1
Final
1
Percentage of In-Term Studies
Percentage of Final Examination
TOTAL
Percentage of Grade
20
40
40
60
40
100
ECTS Workload Table
Activities
Number
Duration(Hour)
Total
Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Laboratory
Application
Field Work
Study Hours Out of Class
Special Course Internship (Work Placement)
Homework Assignments
Quizzes/Studio Critics
Project
Presentations / Seminar
Mid-Terms
Final
Extra Notes
14
3
42
14
8
112
2
15
30
1
1
20
20
Total Workload :
Total Workload / 30(h) :
ECTS Credit :
None
20
20
224
7.47
7.5