訓練學生基礎數理統計推導與證明能力Training students' basic mathematical statistics promotion and certification capabilities
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統計相關課程的能力，課程內容涵概相當的廣度與深度，強調學生能夠了解基本的理論統計概念及在不同情況下的統計程序，課程主題包括機率理論與統計推論，範圍包含：
1. 機率：條件機率、隨機變數、分配函數、期望值、條件期望值
2. 尋找機率分配的技巧：變數變換、動差母函數
3. 分配：離散與連續型分配其特性及分配之間的關係、位置與尺度族、多變量常態分配、t分配和F分配、混合分配
4. 不等式：Chebyshev、Jensen、Hölder、Minkowski
5. 收歛概念與極限分配：不偏性、一致性、機率收斂、分配收斂、強收斂、中央極限定理、Delta方法
6. 隨機樣本：抽樣、單一樣本與兩樣本之信賴區間及假設檢定的常態理論及其相關的大樣本方法、順序統計量、生成隨機樣本技巧、拔靴法
7. 最大概似法及其漸進理論：Cramér-Rao不等式、有效性、最大概似估計量、最大概似估計量的漸近性質、EM演算法、評估點估計量的方法
8. 縮減資料：指數族、充分性、完備性、完備充分統計量、UMVUE、Rao-Blackwell定理、Basu定理
9. 最適假設檢定：Neyman-Pearson引理、MP檢定、UMP檢定、MLR族、UMPU檢定、LR檢定、sequential檢定
10. 區間估計：檢定統計量的轉換、樞紐、評估區間估計量的方法
11. 貝氏方法：決策、貝氏估計量、階層貝氏、經驗貝氏、馬可夫鍊蒙地卡羅法
Mathematical statistics is the core course of students in the Department of Statistics to learn theories of the statistical theory, providing the theoretical foundation of the statistical related courses, and cultivating the ability to practice higher and deeper statistical related courses in the future. The course contents cover a considerable diversity and depth, and emphasizing that students can understand the basic theoretical concepts and statistical procedures under different circumstances. The course topics include probability theory and statistical recommendations, and the scope includes:
1. Opportunity: conditional probability, random variable, allocation function, expected value, conditional expectation value
2. Tips for finding chance allocation: variable change, difference parent function
3. Allocation: the characteristics and relationships between the distribution and the distribution, location and scale families, multivariate constant allocation, t allocation and F allocation, mixed allocation
4. Inequality: Chebyshev, Jensen, Hölder, Minkowski
5. Concept of collection and extreme limit distribution: impartiality, consistency, probability limit, distribution limit, strong limit, central extreme limit theorem, Delta method
6. Random samples: the normal theory of the credibility between sampling, single sample and two samples and the hypothesis confirmation and its related large sample methods, sequence measurement, random sample generation techniques, boot pulling methods
7. Maximum generalized method and its progress theory: Cramér-Rao inequality, validity, maximum generalized similarity estimation, maximum generalized similarity estimation estimation estimation, EM algorithm, method of estimation point estimation
8. Reduce data: index family, sufficiency, completion, full statistics, UMVUE, Rao-Blackwell theorem, Basu theorem
9. The most suitable hypothesis confirmation: Neyman-Pearson lemma, MP confirmation, UMP confirmation, MLR family, UMPU confirmation, LR confirmation, sequential confirmation
10. District estimation: Methods to determine the conversion of statistical measurements, and evaluate the inter-estimation measurements.
11. Beck method: decision, Beck measure, level Beck, test Beck, Markov Montecarrot
Introduction to Mathematical Statistics.
By R.V. Hogg, J. McKean and A.T. Craig
Introduction to Mathematical Statistics.
By R.V. Hogg, J. McKean and A.T. Craig
| 評分項目 Grading Method | 配分比例 Grading percentage | 說明 Description |
|---|---|---|
| 小考小考 Small exam |
20 | |
| 期中考期中考 Midterm exam |
40 | |
| 期末考期末考 Final exam |
40 |
