國立中興大學教學大綱
課程名稱 (中) 數理統計(二)(3332)
(Eng.) Mathematical Statistics (II)
開課單位 應數系
課程類別 必修 學分 3 授課教師 沈宗荏
選課單位 應數系 / 學士班 授課使用語言 中文 英文/EMI 開課學期 1132
課程簡述 提供修課同學對大部分的統計方法能知道其中的原理,更進一步的學會如何發展擁有好性質的估計方法,以及如何評估估計方法之間的優劣。這學期將主要著重在多參數的點估計、假設檢定與信賴區間。
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.

先修課程名稱
課程含自主學習 Y
課程與核心能力關聯配比(%) 課程目標之教學方法與評量方法
課程目標 核心能力 配比(%) 教學方法 評量方法
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.

6.數學、統計、力學之理論解析
100
講授
討論
作業
測驗
其他
授課內容(單元名稱與內容、習作/每週授課、考試進度-共18週)
週次 授課內容
第1週 Review: Point estimation (Maximum Likelihood Methods)

第2週 Point estimation (Multiparameter Case: Estimation)
第3週 Sufficiency
Measures of Quality of Estimators
第4週 Measures of Quality of Estimators
A Sufficient Statistic for a Parameter
第5週 A Sufficient Statistic for a Parameter
Properties of a Sufficient Statistic
第6週 Properties of a Sufficient Statistic
Completeness and Uniqueness
第7週 Completeness and Uniqueness
The Exponential Class of Distributions
第8週 The Exponential Class of Distributions
Functions of a Parameter
第9週 Functions of a Parameter
The Case of Several Parameters
第10週 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
第11週 Minimal Sufficiency and Ancillary Statistics
Sufficiency, Completeness, and Independence
第12週 Sufficiency, Completeness, and Independence
Optimal Tests of Hypotheses: Most Powerful Tests
第13週 Optimal Tests of Hypotheses: Most Powerful Tests
Uniformly Most Powerful Tests
第14週 Uniformly Most Powerful Tests
Likelihood Ratio Tests
第15週 Likelihood Ratio Tests
Bayesian Statistics
第16週 6/5(四) 晚上 6:30-9:00期末考
第17週 6/11(三)上課檢討期末考考卷。
第18週 已提前於第10週白天完成上課。
學習評量方式
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%

教科書&參考書目(書名、作者、書局、代理商、說明)
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
課程教材(教師個人網址請列在本校內之網址)
iLearning
課程輔導時間
TBA

聯合國全球永續發展目標(連結網址)
提供體驗課程:N
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更新日期 西元年/月/日:2025/02/06 10:57:02 列印日期 西元年/月/日:2025 / 3 / 14
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