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課程名稱 |
統計學
Statistics |
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開課學期 |
104-2 |
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授課對象 |
理學院 數學系 |
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授課教師 |
陳 宏 |
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課號 |
MATH3601 |
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課程識別碼 |
201 38100 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期一8,9(15:30~17:20)星期三2(9:10~10:00) |
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上課地點 |
天數304天數304 |
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備註 |
總人數上限：40人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1042MATH3601_statist |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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課程概述 |
Contents:
1. Probability language: Description of random phenomenon, sampling variation,
assessment by simulation, sample mean and variance etc. (Rice Chapters 1, 2, and 3; Wasserman
Chapters 1, 2, and 3)
2. Type of Convergence. Law of Large Numbers, Central limit theorem and Delta Method (Rice
Chapters 4 and 5), Simulation (part of Chapters 8 and 24; Wasserman Chapters 4 and 5, Ch 8.1 and
11.4)
3. Models (Parametric and nonparametric), Fundamental Concepts in Inference including point
estimation, confidence sets, and Hypothesis Testing (Chapter 6)
4. Empirical distribution function (Chapter 7)
5. Resampling: Bootstrap and Jackknife (Wasserman: Chapter 8)
6. Parametric Inference: Estimation and Assumptions Checking (Wasserman: Chapters 9 and 10)
7. Linear and Logistic Regression (Wasserman: Chapter 13)
Topics include: VC theory, convergence, point and interval estimation, hypothesis testing and p-values, data reduction, Bayesian inference, and nonparametric statistics. |
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課程目標 |
Teach the fundamentals of theoretical statistics.
Provide excellent preparation for advanced work in statistics and machine learning.
Introduce the role of statistics in contemporary applications and to develop an elementary understanding of, and fluency in, the statistical paradigm of data collection, exploration, modeling and inference. Inference includes estimation, interval estimation and hypothesis testing.
Both small and large sample theorems of hypothesis testing, interval estimation, and confidence intervals will cover.
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課程要求 |
One year Calculus and 機率導論 or equivalent.
Know the material in Chapters 1-3 of of the book (basic probability). |
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預期每週課後學習時數 |
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Office Hours |
每週三 10:30~12:20
每週一 14:00~15:00 備註： 週一、週三 授課老師 (天文數學大樓465室) ; 週二2-4PM、週五3-5PM，
助教office hour：週四第67節(天文數學館414室) |
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指定閱讀 |
Wasserman (2004). All of Statistics: A Concise Course in Statistical Inference, Springer. http://link.springer.com/book/10.1007/978-0-387-21736-9
Rice, J. A. (2007) Mathematical Statistics and Data Analysis. 3rd edition.
Duxbury. |
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參考書目 |
References:
1. Casella, G. and Berger, R. L. (2002). Statistical Inference. 2nd ed. Duxbury Press. (Textbook for
Advanced Statistical Inference)
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
Homeworks |
30% |
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2. |
Midterm |
30% |
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3. |
Final |
30% |
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4. |
Quizzes |
10% |
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週次 |
日期 |
單元主題 |
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第1週 |
2/22, 2/24 |
Monday: Introduction, concepts, notation
Reading: Wasserman Chapters 1-2.2
Wednesday Reading: Wasserman Chapters 2.3-2.4 |
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第2週 |
3/02 |
No class on Monday, Discrete and Continuous Random Variables (Chapter 2.5-2.6)
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第3週 |
3/7, 3/9 |
Monday: Chapter 2.5-2.7 Wednesday: Chapter 2.8-2.9 |
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第4週 |
3/14, 3/16 |
Cover Chapter 2.9 - 2.12. |
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第5週 |
3/21, 3/23 |
On 23rd, TA will give you an introduction of R program. Complete Chapter 3. |
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第6週 |
3/28, 3/30 |
Ch3.5: Conditional Expectation, Chapter 3.6 Moment Generating Function, Chapter 4 and Chapter 5.1 to 5.3. |
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第7週 |
4/06 |
No class on Monday. Conditional Expectation and Prediction |
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第8週 |
4/11, 4/13 |
4/13: Quiz 1; Chapter 5 Limit Theorem: Law of Large Numbers, Convergence in Distribution and the Central Limit Theorem |
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第9週 |
4/18, 4/20 |
method of maximum likelihood, mode of convergence |
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第10週 |
4/25, 4/27 |
Midterm is given on 4/25; No class on 4/27; For midterm, it covers the materials of Chapters 1 to 5, Chapter 6.3.1, Chapter 7.1, Chapter 9.1-9.5 and 9.7 |
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第11週 |
5/02, 5/04 |
No Class! Convergence in Distribution and the Central Limit Theorem |
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第12週 |
5/09, 5/11 |
Chapter 6.3 Fundamental Concepts in Inference Ch7 Estimating the CDF and Statistical Functional |
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第13週 |
5/16, 5/18 |
Chapter 10 Hypothesis Testing and p-values, |
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第14週 |
5/23, 5/25 |
Chapter 9.8 Optimality, Chapter 9.9 The Delta Method, Chapter 9.10 Multiparameter Models 9.11 Parametric Bootstrap 9.12-9.13 |
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第15週 |
5/30, 6/01 |
Sufficient Statistics, UMVUE |
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第16週 |
6/06, 6/08 |
Chapter 9.8 Optimality, Chapter 9.9 The Delta Method, Chapter 9.10 Multiparameter Models 9.11 Parametric Bootstrap 9.12-9.13 |
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第17週 |
6/13, 6/15 |
Monday: Quiz 2 on hypothesis testing and estimation (Discussion) 6/20 Final Exam
Wednesday: Review on homework. |
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