SM512 ทฤษฎีสถิติ
(Statistical Theory)
ปีการศึกษา 2566
Instructor: รศ. ดร. วีระชาติ กิเลนทอง (tee@riped.utcc.ac.th) และ ดร.สัจจา ดวงชัยอยู่สุข (kei@riped.utcc.ac.th)
Course Schedule: Saturday 9.00 am – 12.00 pm Room 5401
TAs: คุณธนาธร มหาโยธา (ThanathonM.riped@gmail.com)
วิชานี้นำเสนอทฤษฎีและหลักการทางสถิติและความน่าจะเป็นที่จำเป็นสำหรับการวิเคราะห์ทางวิศวกรรมการเงิน โดยเริ่มจากหลักการพื้นฐานของทฤษฎีความน่าจะเป็น (probability theory) ความน่าจะเป็นแบบมีเงื่อนไข (conditional probability) ตัวแปรสุ่มและการแจกแจง (random variables and their distributions) ค่าคาดหมายและโมเมนต์ของตัวแปรสุ่ม (expectation and moments) คุณสมบัติและรูปแบบของการแจกแจงที่ได้รับความนิยมเป็นพิเศษ (special distributions) ทฤษฎีบทสำคัญในทางสถิติ 1) Law of Large Number 2) Central Limit Theorem ซึ่งจะบ่งบอกถึงคุณสมบัติของค่าเฉลี่ยเมื่อกลุ่มตัวอย่างมีขนาดใหญ่มาก การประมาณค่าพารามิเตอร์ด้วยวิธีแบบ maximum likelihood estimation และ Bayes estimation การแจกแจงของตัวประมาณค่า (sampling distributions of estimators) หลักการของการทดสอบสมมุติฐาน (hypothesis testing) และอาจรวมถึงแบบจำลองทางสถิติแบบเชิงเส้น (linear statistical models) วิธีการประมาณค่าแบบ nonparametric
1. Course Objective
The aim of this course is to give master-level students an introduction to principles, theories, and tools in advanced statistical theory. Students will also learn how to apply statistical models with real data using STATA software.
3. Required Textbooks:
1. DeGroot, Morris H. and Mark J. Schervish. 2012. Probability and Statistics. 4th edition: Preason. [DS]
2. Hogg, Robert V., Allen T. Craig and Joseph W. McKean. 2005. Introduction to Mathematical Statistics. 6th edition, Pearson. [HCM]
3.Wooldridge, F.M. (2020). Introductory Econometrics: A Modern Approach (7th Edition). CENGAGE. [W]
Optional Textbooks:
Ross, S. M. (2014). Introduction to Probability Models. Academic press.
Data Sources
We will provide relevant data through the course website: https://sites.google.com/riped.org/tee/teaching/statistics
Program Sources
Program STATA version 14
4. Grades and Requirements
Grades will be based on the following weights:
30% Assignment(s)
30% Mid-Term Exam
40% Final Exam
Tentative Grading Range:
85 – 100 A
80 – 84 B+
70 – 79 B
65 – 69 C+
55 – 64 C
50 – 54 D+
40 – 49 D
39 or less F
4.1. Assignment
Students will be assigned to complete 12-15 individual assignments during the semester. An assignment with the lowest score will be dropped when calculating the total score for each student. Note: Late submission of the assignments is not accepted; a score of zero will be recorded for such assignment.
4.2. Examination
There will be two examinations: a mid-term exam counting for 30% of the total points, and a final exam counting for 40% of the total points. If a student misses a regular examination without acceptable excuse, a score of zero will be recorded for the examination.
Problem Assignments
1. Problem Assignment 1 (Due on September 9 2023 at the beginning of the class).
2. Problem Assignment 2 (Due on September 16, 2023 at the beginning of the class).
3. Problem Assignment 3 (Due on September 23, 2023 at the beginning of the class).
4. Problem Assignment 4 and Dataset for Assignment (Due on September 30, 2023 at the beginning of the class).
5. Problem Assignment 5 (Due on October 7, 2023 at the beginning of the class).
6. Problem Assignment 6 and Dataset for Assignment (Due on October 14, 2023 at the beginning of the class).
7. Problem Assignment 7 and Dataset for Assignment (Due on October 28, 2023 at the beginning of the class).
8. Problem Assignment 8 (Due on November 4, 2023 at the beginning of the class).
9. Problem Assignment 9 (Due on November 11, 2023 at the beginning of the class).
10. Problem Assignment 10 and Dataset for Assignment (Due on November 18, 2023 at the beginning of the class).
11. Problem Assignment 11 (Due on November 25, 2023 at the beginning of the class).
12. Problem Assignment 12 (Due on Decbemer 2, 2023 at the beginning of the class).
13. Problem Assignment 13 and Dataset for Assignment (Due on Decbemer 9, 2023 at the beginning of the class).
14. Problem Assignment 14 and Dataset for Assignment (Due on Decbemer 16, 2023 at the beginning of the class).
15. Problem Assignment 15 and Dataset for Assignment (Due on Decbemer 21, 2023 at the beginning of the class).
Course Schedule
The course will be carried out in 15 sessions, totalling 45 lecture hours. The structure of the course is subject to revision if necessary (e.g., to conform to the background, knowledge, and interests of the students). The tentative structure of the whole course is as follows:
Week 1 (September 2, 2023) : Basic Probability Theory. Reading Materials: Lecture Note.
Week 2 (September 9, 2023) : Conditional Probability. Reading Materials: use the same Lecture Note as week 1.
Week 3 (September 16, 2023) : Random Variables and Distributions. Reading Materials: Lecture Note.
Week 4 (September 23, 2023) : Joint Distributions and Conditional Distributions. Reading Materials: use the same Lecture Note as week 3.
Week 5 (September 30, 2023) : Statistical Independence and Distribution of Function of Random Variables. Reading Materials: use the same Lecture Note as week 3.
Week 6 (October 7, 2023) : Expectation and Variance of Radom Variable. Reading Materials: Lecture Note.
Week 7 (October 14, 2023) : Covariance, Correlation, and Moments. Reading Materials: use the same Lecture Note as week 6.
October 21, 2023 : MIDTERM EXAM (9.00 am to 12.00 pm Room 5401)
Week 8 (October 28, 2023) : Conditional Expectation. Reading Materials: use the same Lecture Note as week 6.
Week 9 (November 4, 2023) : Large-Sample Theories. Reading Materials: Lecture Note.
Week 10 (November 11, 2023) : Normal Distributions and Popular Distributions. Reading Materials: Lecture Note.
Week 11 (November 18, 2023) : Point Estimation: Bayes and MLE Estimations. Reading Materials: Lecture Note.
Week 12 (November 25, 2023) : Hypothesis Testing. Reading Materials: Lecture Note.
Week 13 (December 2, 2023) : Simple Regression Model.
Week 14 (December 9, 2023) : Mutiple Regression Model: Estimation.
Week 15 (December 16, 2023) : Mutiple Regression Model: Inference.
December 23, 2023 : Final EXAM (9.00 am to 12.00 pm Room 5401)
Computer Codes