數理統計(碩)

For this course, I shall try to expose students to as many of the central theoretical ideas and topics in the discipline as possible. Chapters 2 ~ 4 will be covered during the first half semester and Chapters 9, 12, and 17 will be covered during the second half semester. If time is enough, Chapter 7 will be introduced at the end of this semester.

To appreciate this course, students will need a background in advanced calculus, linear algebra, probability, and some analysis. Some of the materials are reviewed in the appendices and Chapters 1, 6, 8, and 16 in the textbook. And, although the content on statistics is reasonably self-contained, prior knowledge of theoretical and applied statistics will be essential.

(1) For the first two weeks, "Asynchronous Distant Learning" will be used for this course. (2) For the third week on, "Asynchronous Distant Learning" or "Learning at Classroom A406" will depend on the requirements of our university. I will upload the relevant information at the e3 digital teaching platform as soon as possible. (3) All the relevant mp4 files for this course will be uploaded to the e3 digital teaching platform when "Asynchronous Distant Learning". Please study them by yourself. If you have any questions, please ask me or teaching assistants by an e-mail or during office hour. (4) The projector and the blackboard will be used for this course when "Learning at Classroom A406".

作業部份: 1. Homework Assignments 1: 15 problems selected from unstarred problems in Chapters 2 ~ 4; due at 1:20 p.m. on Thursday, Nov. 11, 2021 (the 9th week). 2. Homework Assignments 2: 15 problems selected from unstarred problems in Chapters 9, 12, and 17; due at 1:20 p.m. on Thursday, Jan. 13, 2022 (the 18th week). 考試部份: 1. Midterm examination: 5 problems selected from starred problems in Chapters 2 ~ 4; from 1:20 p.m. to 4:20 p.m. on Thursday, Nov. 11, 2021 (the 9th week). 2. Final examination: 5 problems selected from starred problems in Chapters 9, 12, and 17; from 1:20 p.m. to 4:20 p.m. on Thursday, Jan. 13, 2022 (the 18th week). 評量部份: 1. Rollcall: 10%. 2. Homework Assignments 1: 30%. 3. Homework Assignments 2: 30%. 4. Midterm examination: 15%. 5. Final examination: 15%.

• Chapter 2. Exponential Families
• Chapter 3. Risk, Sufficiency, Completeness, and Ancillarity
• Chapter 4. Unbiased Estimation
• Chapter 9. Estimating Equations and Maximum Likelihood
• Chapter 12. Hypothesis Testing
• Chapter 17. Large-Sample Theory for Likelihood Ratio Tests
• Chapter 7. Bayesian Estimation

Textbook: Keener, R. W. (2010), "Theoretical Statistics: Topics for a Core Course", Springer. References: 1. Li, B. and Babu, G. J. (2019), "A Graduate Course on Statistical Inference", Springer. 2. Tattar, P. N., Ramaiah, S., and Manjunath, B. G. (2016), "A Course in Statistics with R", Wiley. The pdf files for these three books can be downloaded from our NYCU library.

地點

A416

時間

Every Tuesday from 1:20 p.m. to 3:10 p.m.

聯絡方式

cchen@stat.nctu.edu.tw (03)571-2121 Ext. 31794 or (03)573-1794