| Relevance of Course Objectives and Core Learning Outcomes(%) |
Teaching and Assessment Methods for Course Objectives |
| Course Objectives |
Competency Indicators |
Ratio(%) |
Teaching Methods |
Assessment Methods |
The goal of this course is to provide students with a theoretical foundation in key statistical methods. Students will learn how to develop estimation methods with desirable properties and compare different estimation approaches based on their statistical characteristics. The course will primarily focus on point estimation, confidence interval estimation, and statistical hypothesis testing.
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| 6.Theory of Mathematical Analysis, Statistics, and Mechanics |
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| Course Content and Homework/Schedule/Tests Schedule |
| Week |
Course Content |
| Week 1 |
Review: Point estimation (Maximum Likelihood Methods)
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| Week 2 |
Point estimation (Multiparameter Case: Estimation) |
| Week 3 |
Sufficiency
Measures of Quality of Estimators |
| Week 4 |
Measures of Quality of Estimators
A Sufficient Statistic for a Parameter |
| Week 5 |
A Sufficient Statistic for a Parameter
Properties of a Sufficient Statistic |
| Week 6 |
Properties of a Sufficient Statistic
Completeness and Uniqueness |
| Week 7 |
Completeness and Uniqueness
The Exponential Class of Distributions |
| Week 8 |
The Exponential Class of Distributions
Functions of a Parameter |
| Week 9 |
Functions of a Parameter
The Case of Several Parameters |
| Week 10 |
4/24(四) 晚上 6:30-9:00期中考，當週白天繼續上課，補第18周的課
The Case of Several Parameters
Minimal Sufficiency and Ancillary Statistics |
| Week 11 |
Minimal Sufficiency and Ancillary Statistics
Sufficiency, Completeness, and Independence |
| Week 12 |
Sufficiency, Completeness, and Independence
Optimal Tests of Hypotheses: Most Powerful Tests |
| Week 13 |
Optimal Tests of Hypotheses: Most Powerful Tests
Uniformly Most Powerful Tests |
| Week 14 |
Uniformly Most Powerful Tests
Likelihood Ratio Tests |
| Week 15 |
Likelihood Ratio Tests
Bayesian Statistics |
| Week 16 |
6/5(四) 晚上 6:30-9:00期末考 |
| Week 17 |
6/11(三)上課檢討期末考考卷。 |
| Week 18 |
已提前於第10週白天完成上課。 |
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| Evaluation |
Grading:
Midterm exam (April 6, 2025 during 18:30-21:00): 35%
Terminal exam (June 9, 2025 during 18:30-21:00): 35%
Miscellanea (including homework, quizzes, class presence etc.): 30%
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| Textbook & other References |
Text: Introduction to Mathematical Statistics, 8th Edition, by Robert V. Hogg, Joseph W. Mckean and
Allen T. Craig.
References:
1. An Introduction to Probability and Statistics, 2nd Edition, by Vijay K. Rohatgi and A. K. Md. Ehsanes Saleh
2. Introduction to Probability and Statistical Inference, First Edition, by George Roussas
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| Teaching Aids & Teacher's Website |
| iLearning |
| Office Hours |
TBA
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| Sustainable Development Goals, SDGs(Link URL) |
| include experience courses：N |
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