This course aims to teach the students statistical inference.
The first semester will cover introductory of probability,
properties of the cumulative distribution function (univariate and multivariate), moment
generating function, some special distribution, joint distribution,
conditional distribution, the elementary statistical inference,
order statistics, point estimation, interval estimation, consistency and the central limit theorem.This course aims to teach the students statistical inference.
The first semester will cover introduction of probability,
properties of the cumulative distribution function (univariate and multivariate), moment
generating function, some special distribution, joint distribution,
conditional distribution, the elementary statistical inference,
order statistics, point estimation, interval estimation, consistency and the central limit theorem.
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，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，為能獲得較佳的學習成效，學生應具備微積分與機率論的基礎，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
5.隨機樣本收歛概念與極限分配：不偏性、一致性、機率收斂、分配收斂、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
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
Mathematical statistics are the core courses for students in the Department of Statistics to learn the theoretical foundation of the statistical related courses, and cultivate the ability to practice higher and more profound courses in the future. The course content covers the considerable diversity and depth, and emphasizes the Students can understand the basic theoretical concepts and statistical procedures under different circumstances. In order to achieve better learning results, students should have the basics of micro-scores and probability discussions. 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 of scattered and continuous distribution, location and scale families, multivariate constant allocation, t allocation and F allocation, mixed allocation
4. Inequality: Chebyshev, Jensen, Hölder
5. Random sample collection concept and extreme limit allocation: impartiality, consistency, probability limit, allocation 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 general analogy method and its progress theory: Cramér-Rao inequality, validity, maximum general similarity estimation, maximum general similarity estimation estimation estimation proximity, EM algorithm
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
Introduction of Mathematical Statistics,
eight edition. (Hogg, Mckean and Craig)
Introduction of mathematical statistics,
| 評分項目 Grading Method | 配分比例 Grading percentage | 說明 Description |
|---|---|---|
| midtermmidterm midterm |
50 | |
| finalfinal Final |
50 |
