Mathematical Statistics Course Information

Wu: mathstat97

數理統計 (Mathematical Statistics)

開課學期：97 學年度上、下學期
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 3 節 (B617)
助教實習：星期四第 9, 10 節（胡珮蓉助教）

授課老師：

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

先修科目：機率論

教科書：

Roussas, G. G. (1997). A Course in Mathematical Statistics, 2nd ed., Academic Press. (Chapters 8, 11, 12, 13, 15)

推薦參考書籍：

Hogg, R. V., McKean, J. W. and Craig, A. T. (2005). Introduction to Mathematical Statistics, 6th ed., Prentice Hall. (Chapters 4 - 8, 11)

參考書籍：

Hogg, R. V. and Craig, A. T. (1995). Introduction to Mathematical Statistics, 5th ed., Prentice Hall. (Chapters 5 - 9)
Larsen, R. J. and Marx, M. L. (2006). An Introduction to Mathematical Statistics and Its Applications, 4th edition, Prentice Hall.
Mood, A. M., Graybill, F. A. and Boes, D. C. (1974). Introduction to the Theory of Statistics, 3rd ed., McGraw-Hill. (Chapters VII - IX)
Wackerly, D. D., Mendenhall, W. and Scheaffer, R. L. (2007). Mathematical Statistics with Applications, 7th edition, Duxbury.

主題：

上學期：

Basic limit theorems (Chapter 8)
Point estimations (Chapters 11, 12 (Family of distributions, Sufficiency, Completeness, Method of moments, MLE))

下學期：

Point estimations (Chapters 11, 12 (Unbiasedness, UMVUE, CRLB, Asymptotic properties, Bayes estimator, Minimax estimator))
Confidence intervals (Chapter 15)
Testing hypotheses (Chapter 13)

評分方法：

助教實習： 20% (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)
小考一： 10% (期中考前二至四週於助教實習課舉行，未參加者以零分計算，不接受補考)
小考二： 10% (期末考前二至四週於助教實習課舉行，未參加者以零分計算，不接受補考)
期中考： 20%
期末考： 30%

練習作業：

機率論部分：
Limit Theorems (Chapter 8)	Convergence in Distribution	8.2.2, 8.2.3, 8.3.12, 8.3.14, 補充習題 (Chapter 5 in Hogg & Craig (1995)): 5.1, 5.2, 5.3, 5.5, 5.6, 5.11, 5.12, 5.14, 5.15, 5.17, 5.18, 5.31
	Convergence in Probability	8.1.1, 8.1.5, 8.4.1, 8.4.3, 8.4.4, 8.4.5, 8.4.6, 8.4.7, 補充習題 (Chapter 5 in Hogg & Craig (1995)): 5.7, 5.8, 5.9, 5.10
	Convergence in the r-th Mean	8.1.3, 8.1.4
	Further Limit Theorems	9.2.8(iv), 9.2.13, 補充習題 (Chapter 5 in Hogg & Craig (1995)): 5.33, 5.34, 5.35

統計推論部分：
Point Estimation (Chapters 11, 12)	Family of Distributions	11.1.1, 11.4.1, 11.5.1, 11.5.2
	Sufficiency	11.1.2, 11.1.3, 11.1.5, 11.1.6, 11.1.7, 11.1.8, 11.1.10
	Completeness	11.2.1, 11.2.2, 11.4.2, 11.4.3, 11.5.3(ii)
	Method of Moments	12.9.1, 12.9.2, 12.9.3, 12.9.4, 12.9.5
	MLE	12.5.1, 12.5.2, 12.5.3, 12.5.7, 12.5.8, 12.5.9, 12.5.10
	Unbiasedness	12.2.1, 12.2.2, 12.2.3, 12.2.4, 12.2.6, 12.2.7
	UMVUE	11.3.1, 12.3.3, 12.3.4, 12.3.6, 12.3.7, 12.3.8, 12.3.9, 12.3.11, 12.3.12, 12.3.13
	CRLB	12.4.1, 12.4.2, 12.4.3, 12.4.4, 12.4.5, 12.4.8
	Asymptotic Properties	12.10.1, 12.11.1, 12.11.2, 12.11.3
	Risk and Minimax	補充習題 (Chapter 7 in Hogg & Craig (1995)): 7.6, 7.7, 7.8
	Bayes Estimator	12.7.1(i) (iii), 12.7.2(i) (iii), 12.7.3(i) (iii) (iv), 12.7.4(i) (iii) (iv) (v)
Confidence Intervals (Chapter 15)		15.2.1, 15.2.2, 15.2.3, 15.2.4, 15.2.5, 15.2.7, 15.2.8, 15.2.9, 15.2.10, 15.3.1, 15.4,1, 15.4.2, 15.4.3, 15.4.6, 15.4.7
Testing Hypotheses (Chapter 13)	MP tests	13.1.1, 13.2.1, 13.2.2, 13.2.3, 13.2.4, 13.2.5, 13.2.7
	UMP tests	13.3.1, 13.3.2, 13.3.5, 13.3.6, 13.3.8, 13.3.9, 13.3.11, 13.3.12
	UMPU tests	13.4.1, 13.4.2
	LR tests	13.7.1, 13.7.2, 13.7.3, 13.7.4

Last modified: 18:11:30 Monday September 1, 2008 by Shuo-Jye Wu