Mathematical Statistics Course Information

Wu: mathstat112

數理統計 (Mathematical Statistics)

開課學期：112 學年度第 1、2 學期
開課班級：統計三B
學分數：3/3
上課時間：

星期二第 3, 4 節 (B617)、星期三第 4 節 (B617)
助教實習：星期二第 1, 2 節（蘇建郎助教）

授課老師：

吳碩傑
Office: B831
Tel: 2621-5656 Ext. 2886
E-mail: shuo@mail.tku.edu.tw
Webpage http://www1.stat.tku.edu.tw/~shuo/

先修科目：微積分、機率論

教科書：

Roussas, G. G. (2015). An Introduction to Probability and Statistical Inference, 2nd edition, Academic Press. (Chapters 7 - 11)

推薦參考書籍：

Hogg, R. V. and Craig, A. T. (1995). Introduction to Mathematical Statistics, 5th edition, Prentice Hall. (Chapters 5 - 9)
Roussas, G. G. (1997). A Course in Mathematical Statistics, 2nd edition, Academic Press. (Chapters 8, 11, 12, 13, 15)

參考書籍：

Mood, A. M., Graybill, F. A. and Boes, D. C. (1974). Introduction to the Theory of Statistics, 3rd edition, McGraw-Hill. (Chapters VII - IX)
Wackerly, D. D., Mendenhall, W. and Scheaffer, R. L. (2008). Mathematical Statistics with Applications, 7th edition, Brooks/Cole Cengage Learning. (Chapters 8 - 10, 16)

主題：

上學期：

Basic limit theorems
Family of distributions (Exponential family, Location and Scale Families)
Data reduction (Sufficiency, Ancillary, Completeness)
Point estimation
- Methods of finding estimators (Method of moments, Method of maximum likelihood, etc.)
- Methods of evaluating estimators (Unbiasedness, UMVUE)

下學期：

Point estimation
- Methods of evaluating estimators (CRLB, Asymptotic properties)
- Decision-theoretic approach (Minimax estimator, Bayes estimator)
Interval estimation
- Methods of finding interval estimators (Pivotal quantities, Pivoting the CDF, inverting a test statistic)
- Methods of evaluating interval estimators (The shortest expected length confidence interval)
Testing hypotheses
- Methods of finding tests (LR tests)
- Methods of evaluating tests (MP tests, UMP tests, UMPU tests)

評分方法：

助教實習： 25% （凡修本課程者一律必須上實習課，否則助教實習分數以零分計算）
複習考： 10% （開學第二週於助教實習課舉行，未參加者以零分計算，不接受補考。若第二週遇國定假日，則提前至第一週舉行）
期中考： 30%
期末考： 35%
本課程沒有點名分數，也沒有任何點名加分機制，請不要有無缺課就會及格或不擋修的想法！

練習作業：

機率論部分：
Limit Theorems	Convergence in Distribution	7.1.1, 7.1.3, 7.1.5, 7.2.3, 7.2.8, 7.2.9, 7.2.11, 7.2.13, 7.2.17, 7.2.19, 7.2.20, 7.2.22, 7.2.23, 7.2.24, 7.2.25, 7.2.32
	Convergence in Probability	7.1.2, 7.1.4, 7.2.1, 7.2.2, 7.3.1, 7.3.2
	Convergence in the r-th Mean	7.1.6, 7.1.8
	Further Limit Theorems	7.1.10, Roussas (1997): 9.2.8(iv), 9.2.13; Hogg and Craig (1995): 5.33, 5.34, 5.35

統計推論部分：
Family of Distributions	Basic Concepts	Roussas (1997): 11.1.1
	Exponential Family	Roussas (1997): 11.4.1, 11.5.1, 11.5.2
	Location and Scale Families
Data Reduction	Sufficiency	9.2.6, 9.2.7, 9.2.8, 9.2.11
	Ancillary	Hogg and Craig (1995): 7.56
	Completeness	Hogg and Craig (1995): 7.23, 7.24, 7.51(a), 7.57, 7.58, 7.61, 7.65, 7.66
Point Estimation	Method of Moments	9.5.1, 9.5.2(i), 9.5.3, 9.5.5, 9.5.6, 9.5.7, 9.5.8, 9.5.9
	Method of Maximum Likelihood	9.1.5, 9.1.6, 9.1.7, 9.1.8, 9.1.9, 9.1.10, 9.1.11, 9.2.1, 9.2.2, 9.2.3, 9.2.4, 9.2.5, 9.5.1
	Unbiasedness	9.3.1, 9.3.2, 9.3.3, 9.3.4, 9.3.5, 9.3.8, 9.3.9
	UMVUE	9.3.11, 9.3.12, 9.3.18, 9.3.19
	CRLB	9.3.13, 9.3.14, 9.3.15, 9.3.20
	Asymptotic Properties	9.5.12, Hogg and Craig (1995): 6.6, 6.7, 8.17
	Risk	Hogg and Craig (1995): 7.6, 7.7, 7.8
	Bayes Estimator	9.4.1, 9.4.4
	Minimax Estimator	9.4.6
Confidence Intervals		10.1.1, 10.1.2, 10.1.5, 10.1.6, 10.1.7, 10.1.8, 10.1.9, 10.1.11, 10.1.12, 10.1.17, 10.1.18, 10.1.19 (additional exercises if time permits: 10.2.1, 10.4.1, 10.4.2, 10.4.3)
Testing Hypotheses	Basic Concepts	11.1.1, 11.1.2
	MP tests	11.2.1, 11.2.2, 11.2.3, 11.2.4, 11.2.5, 11.2.7, 11.2.8
	UMP tests	11.3.2, 11.3.5, 11.3.6, 11.3.7, 11.3.8, 11.3.10, 11.3.12, 11.3.14, 11.3.15
	UMPU tests	Roussas (1997): 13.4.1, 13.4.2
	LR tests	11.4.1, 11.4.2, 11.4.3, 11.4.4, 11.4.6, 11.4.11, 11.4.12, 11.4.13

Last modified: 14:04:30 Friday June 30, 2023 by Shuo-Jye Wu