數理統計為統計系學生學習統計理論的核心課程，提供統計相關課程的理論根基，並且培養未來修習更高深與統計相關之課程的能力，下學期課程主題以統計推論為主，範圍包含：1. 隨機樣本：極限分配及其常態理論、順序統計量、生成隨機樣本技巧 2. 點估計量：最大概似法及其漸進理論、EM演算法、指數族 3. 點估計量之評比：完備充分統計量、MVUE 4. 檢定：NP引理、MP檢定、UMP檢定、MLR族、UMPU檢定、LR檢定。Mathematical statistics is a core course for statistics students to learn statistical theory, providing a theoretical foundation for statistics-related courses and cultivating the ability to take more advanced statistics-related courses in the future. The course topics for the next semester will be mainly statistical inference, and the scope includes: 1. Random samples: limit distribution and its normality theory, sequential statistics, techniques for generating random samples 2. Point estimators: maximum approximation method and its asymptotic theory, EM algorithm, exponential family 3. Evaluation of point estimators: complete and sufficient statistics Quantity, MVUE 4. Test: NP lemma, MP test, UMP test, MLR family, UMPU test, LR test.
1. Hogg RV, McKean JW, Craig AT (2013) Introduction to Mathematical Statistics (7/E), Pearson Prentice Hall.
1. ho GG RV, McKean JW, Craig at (2013) Introduction to mathematical statistics (7/E), Pearson Prentice hall.
| 評分項目 Grading Method | 配分比例 Grading percentage | 說明 Description |
|---|---|---|
| Midterm ExamMidterm Exam midterm exam |
33 | |
| Final ExamFinal Exam final exam |
34 | |
| Quizzes and Recitation ClassQuizzes and Recitation Class quizzes and recitation classes |
33 | 4 ~ 5 quizzes |
