高等統計推論一、二
課程安排
Note: Prediction is difficult, especially with respect to the future. As a result, listings of plans for classes, and of homework, are always subject to change. To be sure you're preparing the right homework, doing the right readings, etc.... check this page regularly. Often, homework assignments in particular will change --- either because of a small change to the assignment, or because I didn't get as far in class as I had planned and hence have to change (usually reduce) the assignment.
Note: Class meets Wednesday 1:00 - 2:50 and Friday 11:20-12:10 in 新數102 except where otherwise noted.
Instructor: 陳宏 舊數106 Email: hchen@math.ntu.edu.tw Phone#: 3366-2846
Office hours: Wednesday 11-12/Friday 10:20-11:00, or by appointment
Teaching Assistant: 黃信雄 Email: r93221018@ntu.edu.tw Office hours: Friday afternoon
The objective of this course is to introduce to the students some basic theory of probability. It is fundamentally important for understanding the commonly used statistical concepts and methods. It also provides a necessary basis for students for a further study of other advanced statistical courses.
Outline
Fall semester:
1. Probabilities, random variables, and distributions.
2.
Transformations and expectations.
3. Common families of distributions.
4.
Multivariate probability distributions and related properties.
5. Random
samples, sampling distributions, and convergence concepts.
6. Sufficiency,
likelihood, and equivalence principles.
Spring semester
Chapter 9: (2 weeks) Interval estimation
Inverting method, pivotal quantity, p-value,
Bayesian interval estimates
Bayes procedure, decision and prediction theory:
Loss and risk function, 23
Bayes rules, minimax principle, optimal decision
rules, predictive distribution
Chapter 10: (3 weeks) Asymptotic methods
Consistency and efficiency of MLE, Bootstrap approach
Robustness, Huber estimator, Robustness of
sample mean,
sample median, and M-estimator
Wald and Score statistic
Chapter 11, 12: (1 week) Topics of Linear model, generalized linear model and logistic model
Text: Statistical Inference, Second Edition, Casella and
Berger
• Chapters 1-6 of Casella and Berger will form the basis of the
course.
The following books provide supplementary reading and additional examples.
1. Rice, John A. (1995). Mathematical Statistics and Data Analysis. 2nd
edition. Duxbury Press.
2. Bickel, P.J., and Doksum, K.A. (2001).
Mathematical Statistics: Basic Ideas and Selected Topics, Vol. I. 2nd edition
Prentice Hall.
3. Lehmann, E. L. and Casella, G. (1998). Theory of Point
Estimation. 2nd Edition, Springer.
Homework 1: Chapter 1, Due date: 10/07/05 Solution
Homework 2: Chapter 2, Due date: 10/19/05 Solution
Homework 3: Chapter 3, Due date: 11/09/05 Solution
Homework 4: Chapter 4, Due date: 11/30/05 Solution
Homework 5: Chapter 5, Due date: ?/07/05 Solution
Homework 6: Chapter 6, Due date: ?/07/06 Solution
Homework 7: Chapter 7, Due date: ?/?/06 Solution
Homework 8: Chapter 8, Due date: ?/?/06 Solution
Homework 9: Chapter 9, Due date: ?/?/06 Solution
Homework 10: Chapter 10, Due date: ?/?/06 Solution
Homework 11: Chapter 11, Due date: ?/?/06 Solution
Homework 12: Chapter 12, Due date: Solution
課程內容及進度
September October November December January February March April May June
February 2006
| ||||||
Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday |
1 | 2 | 3 | 4 | |||
5 | 6 | 7 |
8 |
9 | 10 | 11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
19 |
20 學期 上課開始 |
21 |
22 Class Sufficient Principle ch6 |
23 |
24 Class Likelihood Principle |
25 |
26 |
27 |
28和平紀念日 |
|
|
March 2006
| ||||||
Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday |
1 Class Equivalence Principle | 2 | 3 Class Point Estimation | 4 | |||
5 | 6 加退選 |
7 |
8 Class Point Estimation |
9 | 10 Class Point Estimation | 11 |
12 |
13 |
14 |
15 Class Point Estimation |
16 |
17 Class Point Estimation |
18 |
19 |
20 |
21 |
22 Class Point Estimation |
23 |
25 | |
26 |
27 |
28 |
29 Class Asymptotic methods 4 |
30 |
31 Class
Asymptotic methods 6
|
|
April 2006
| ||||||
Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday |
1 | ||||||
2 | 3 | 4 |
5民族掃墓節 |
6 | 7 Class Asymptotic methods | 8 |
9 |
10 |
11 |
12 Class
Asymptotic methods |
13 |
14 Class
Asymptotic methods |
15 |
16 |
17 期中考週 |
18 |
19 Class Asymptotic methods Overview |
20 |
21 Class Asymptotic methods 3 |
22 |
23/30 |
24 |
25 |
26 Class Test of hypothesis 4 |
27 |
29 |
May 2006
| ||||||
Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday |
1 | 2 | 3 Class Test of hypothesis | 4 | 5 Class Test of hypothesis | 6 | |
7 |
8 | 9 | 10 Class Test of hypothesis | 11 |
12 Class Test of hypothesis |
13 |
14 |
15 |
16 |
17 Class
Interval estimation |
18 | 19 Class Interval estimation | 20 |
21 |
22 |
23 |
24 Class linear model |
25 |
26 Class linear model B3 |
27 |
28 |
29 |
30 |
31 端午節 |
|
|
|
June 2006
| ||||||
Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday |
1 | 2 Class | 3 | ||||
4 | 5 | 6 |
7 Class |
8 | 9 Class | 10 |
11 |
12 |
13 |
14 Class |
15 |
16 Class |
17 |
18 |
19 |
20 |
21 期末考 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30
|
|
September 2005
| ||||||
Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday |
1 | 2 | 3 | ||||
4 | 5 | 6 |
7 |
8 | 9 | 10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18中秋節 |
19 學期 上課開始 |
20 |
21 Class Overview Set Theory 1 |
22 |
24 | |
25 |
26 |
27 |
28 Class Conditional Probability and Independence 4 |
29 |
|
October 2005
Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday |
2 |
3 |
4 |
6 |
7 Class Expected values 8 |
8 | |
9 |
10 國慶 紀念日 |
11 |
|
13 |
14 Class Differentiating under an integral sign
|
15 |
16 |
17 |
18 |
|
20 |
21 Class Discrete Distribution 16 |
22 |
23 |
24 |
25 |
26 Class Summary |
27 |
28 Class Continuous Distribution 19 |
29 |
30 |
30 |
31 |
|
Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday |
|
|
1 |
3 |
4 Class Inequalities and Identities 21 |
5 | |
6 |
7 期中考 試開始 |
8 |
9 Class: Review 2nd homework. Multiple Random Variables 22 |
10 |
11 Class Quiz 1
|
12 |
13 |
14 |
15 停課 一天 |
16 Class Multiple Random Variables 23 |
17
|
18 Class
Transformations 24 |
19 |
20 |
21 |
22 |
23 Midterm
|
24
|
26 | |
27 |
28 |
29 |
30 Class Quiz 2
|
|
|
|
Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday |
1 |
3 | |||||
4 |
5 |
6 |
8 |
10 | ||
11 |
12 |
13 |
15 |
16 Class Generating a random sample
|
17 | |
18 |
19 |
20 |
21 Class
|
22 |
23 Class
|
24 |
25 |
26 |
27 |
28 Class |
29 |
30 Class |
31 |
Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday |
1 |
2 | 3 | 4
Class Summary
|
5 |
6
Class Review 上課最後一天 |
7 |
8 |
9 |
10 |
11 期末考 |
12 |
13 |
14 |
15 |
16 寒假開始 |
17 |
18
|
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 除夕 |
29 |
30 |
31 |
1. Optimization (convex and constrained optimization) See Lecture Notes 1, 2, 3, 10
at http://www.princeton.edu/~chiangm/class.html.
2. Linear algebra: Professor Strang's Class 18.06 Linear Algebra Lecture Videos, Fall 1999
(可由網路取得)at
Download at http://cran.cs.pu.edu.tw/ or http://cran.csie.ntu.edu.tw/
Look for Precompiled Binary Distributions Windows (95 and later)
Look for base. Download rw2011.exe