Type of Credit: Required
Credit(s)
Number of Students
This course provides students with the principles of probability theory and the theory of statistical inference, such as estimation methods, confidence intervals, and hypothesis testing procedures.
Those topics are essential for graduate students for further development in the field of Statistics or related fields.
能力項目說明
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The students will be able to make theoretical derivations and works on the following topics: 1. Point estimation methods 2. Properties of point estimates 3. Asymptotic properties of point estimates 4. Hypothesis testing methods and properties 5. Interval estimation methods |
| 教學週次Course Week | 彈性補充教學週次Flexible Supplemental Instruction Week | 彈性補充教學類別Flexible Supplemental Instruction Type |
|---|---|---|
|
週次 |
課程主題 |
課程內容與指定閱讀 |
教學活動與作業 |
|
|
1 |
Principles of Data Reduction |
6.1, 6.2 |
6.1-6.30 |
|
|
2 |
Complete Sufficient Statistics, MME, MLE |
6.2, 7.1,7.2 |
6.31, 6.36, 6.37, 6.40, 7.1-7.14(HW1) |
|
|
3 |
MLE, Bayes Estimators |
7.2 |
7.15-7.26, 7.32 |
|
|
4 |
MSE, Best Unbiased, Sufficiency and Unbiasedness |
7.3 |
7.33, 7.38-7.45 |
|
|
5 |
Loss Function Optimality, EM |
7.3, 7.2 |
7.46-7.65(HW2) |
|
|
6 |
Asymptotic about point estimators |
10.1 |
10.1-10.11, 10.16 |
|
|
7 |
Holiday |
Review for midterm |
|
|
|
8 |
Point estimators + Robustness |
10.2.1 |
10.18-10.23 |
|
|
9 |
Midterm |
(Ch. 6, Ch. 7, 10.1, 10.2.1) |
Review for midterm |
|
|
10 |
Methods of finding tests |
8.1, 8.2 |
8.1-8.24(HW3) |
|
|
11 |
Methods of finding and evaluating tests |
8.2, 8.3 |
8.25-8.36 |
|
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12 |
Methods of finding and evaluating tests |
8.3 |
8.37-8.46, 8.48, 8.47, 8.49, 8.51, 8.52 |
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|
13 |
Asymptotic about tests Methods of finding interval estimators |
10.3; 9.1, 9.2 |
10.31-10.38 (HW4) |
|
|
14 |
Methods of finding interval estimators Asymptotic intervals |
9.2, 10.4 |
9.1, 9.2, 9.58(a), 9.3-9.15,9.16-9.25, 9.34, 9.35, 9.36,10.4:10.40-10.43, 10.47 |
|
|
15 |
Asymptotic intervals, Evaluating interval estimators |
10.4, 9.3 |
10.4:10.40-10.43, 10.47, 9.37-9.41, 9.44-9.52, 9.56-9.58(HW5) |
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16 |
Review |
Review for Final |
Review for Final |
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17 |
Final Exam |
(8.1-8.3, 10.3, 9.1-9.3, 10.4) |
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Statistical inference, second edution; George Casella and Roger L. Berger