Advanced Statistical Inference I & II

高等統計推論一

Class Calendar

課程安排

Last updated 2/13/2006 (Established in July 2005)

Note: Prediction is difficult, especially with respect to the future. As a result, listings of plans for classes, and of homework, are always subject to change. To be sure you're preparing the right homework, doing the right readings, etc.... check this page regularly. Often, homework assignments in particular will change --- either because of a small change to the assignment, or because I didn't get as far in class as I had planned and hence have to change (usually reduce) the assignment.


Note: Class meets Wednesday 1:00 - 2:50 and Friday 11:20-12:10 in 新數102 except where otherwise noted.

Instructor: 陳宏  舊數106   Email: hchen@math.ntu.edu.tw  Phone#: 3366-2846

      Office hours:  Wednesday 11-12/Friday 10:20-11:00, or by appointment

Teaching Assistant:  黃信雄           Email:  r93221018@ntu.edu.tw     Office hours:  Friday afternoon

成績評量方式

  • 習題(20%每一章指定一次每次應該不超過10題)
  • 期中考(30%
  • 期末考(30%
  • 小  考 (20%)

    The objective of this course is to introduce to the students some basic theory of probability. It is fundamentally important for understanding  the commonly used statistical concepts and methods. It also provides a necessary basis for students for a further study of other advanced statistical courses.

    Outline

    Fall semester:

    1. Probabilities, random variables, and distributions.
    2. Transformations and expectations.
    3. Common families of distributions.
    4. Multivariate probability distributions and related properties.
    5. Random samples, sampling distributions, and convergence concepts.
    6. Sufficiency, likelihood, and equivalence principles.

    Spring semester

    Chapter 7: (4 weeks) Point Estimation

    Chapter 8: (3 weeks) Test of hypothesis

    Chapter 9: (2 weeks) Interval estimation

    Chapter 10: (3 weeks) Asymptotic methods

    Chapter 11, 12: (1 week) Topics of Linear model, generalized linear model and logistic model

     

     

    Text: Statistical Inference, Second Edition, Casella and Berger
    • Chapters 1-6 of Casella and Berger will form the basis of the course.

    The following books provide supplementary reading and additional examples.

    1. Rice, John A. (1995). Mathematical Statistics and Data Analysis. 2nd edition. Duxbury Press.
    2. Bickel, P.J., and Doksum, K.A. (2001). Mathematical Statistics: Basic Ideas and Selected Topics, Vol. I. 2nd edition Prentice Hall.
    3. Lehmann, E. L. and Casella, G. (1998). Theory of Point Estimation. 2nd Edition, Springer.

     

    Homework Assignment

    課程內容及進度

    September  October    November    December   January  February  March  April   May June

    February 2006


     
     Sunday Monday Tuesday Wednesday Thursday Friday Saturday
          1  2  3  4
    5 6 7
     8
     9  10  11
    12
    13
    14
    15
    16
    17
     18
    19

    20 學期

    上課開始

    21

    22 Class Sufficient Principle ch6

    23

    24 Class

    Likelihood Principle

     25
    26

    27

    28和平紀念日

     
       
     

  • March 2006


     
     Sunday Monday Tuesday Wednesday Thursday Friday Saturday
          1 Class Equivalence Principle  2  3 Class Point Estimation  4
    5 6

    加退選

    7
     8  Class Point Estimation
     9  10 Class  Point Estimation  11
    12
    13
    14
    15 Class Point Estimation
    16
    17 Class Point Estimation
     18
    19

    20  

    21

    22 Class Point Estimation  

    23

    24Class Point Estimation  2 & 3

     25
    26

    27

    28

    29  Class

    Asymptotic methods   4

    30
    31 Class Asymptotic methods 6

     

     

    April 2006


     
     Sunday Monday Tuesday Wednesday Thursday Friday Saturday
                 1
    2 3 4
     5民族掃墓節
     6  7 Class  Asymptotic methods  8
    9
    10
    11
    12  Class  Asymptotic methods
    13
    14 Class  Asymptotic methods
     15
    16

    17 期中考週

    18

    19 Class Asymptotic methods Overview  

    20

    21 Class Asymptotic methods 3

     22
    23/30

    24

    25

    26  Class  Test of hypothesis  4

    27
    28 Class Test of hypothesis  6

     

    29

    May 2006


     
     Sunday Monday Tuesday Wednesday Thursday Friday Saturday
       1  2  3  Class Test of hypothesis 4 Class  Test of hypothesis 6
     7
     8  9  10   Class Test of hypothesis 11
    12 Class  Test of hypothesis
    13
    14
    15
    16
     17 Class  Interval estimation
    18 19  Class  Interval estimation 20
    21

    22

    23

    24 Class   linear model

    25

    26 Class  linear model B3

     27
    28

    29

    30

    31  端午節

     

     

     

    June 2006


     
     Sunday Monday Tuesday Wednesday Thursday Friday Saturday
             1  2  Class  3
    4 5 6
     7   Class
     8  9  Class  10
    11
    12
    13
    14   Class
    15
    16  Class
     17
    18

    19  

    20

    21 期末考

    22

    23

     24
    25

    26

    27

    28

    29
    30

     

     

     September 2005


     
     Sunday Monday Tuesday Wednesday Thursday Friday Saturday
             1  2  3
    4 5 6
     7
     8  9  10
    11
    12
    13
    14
    15
    16
     17
    18中秋節

    19 學期

    上課開始

    20

    21 Class Overview  

    Set Theory 1

    22

    23 Class

    Basics of Probability Theory 2 & 3

     24
    25

    26

    27

    28  Class

    Conditional Probability and Independence 4

    29
    30 Class

    Random Variable 5

    Density and Mass Functions 6

     

     

    October 2005

     

     Sunday Monday Tuesday Wednesday Thursday Friday Saturday
      2

      3

    4

      5 Class

    Distributions of Functions of a Random Variable 7

     

       Summary

      6

      7 Class

    Expected values 8

      8
      9

    10 國慶

      紀念日

    11

    12 Class  Summary

    Moments and moment generating functions 9

     

    13

    14 Class

    Differentiating under an integral sign

     

    15
     16

    17

    18

    19 Class  Summary

    Discrete Distribution 11  & 12 & 13

     

    20

    21 Class

    Discrete Distribution 16

    22
     23

    24

    25

    26 Class  Summary

    Continuous Distribution 17 & 18

    27

    28 Class

    Continuous Distribution 19

    29
     30

    30

    31 
     
         
     

    November 2005


     
     Sunday Monday Tuesday Wednesday Thursday Friday Saturday
     

     

      1 

      2 Class 

    Exponential Families

    Location and Scale Families 20

      3

      4 Class

    Inequalities and Identities 21

      5
      6

      7  期中考

       試開始

     

      8

      9 Class: Review 2nd homework.

    Multiple Random Variables 22 

    10
    11  Class Quiz 1

     

     

    12
    13

    14

    15 停課

      一天

    16 Class 

    Multiple Random Variables 23

    17

     

    18  Class

    Transformations 24

    19
    20

    21

    22

    23 Midterm

     

    24

     

    25  Class 

    Hierarchical Models and Mixture Distributions 26 & 27

    26
    27

    28

    29

    30 Class  Quiz 2

     

     
     
     

     December 2005


     Sunday Monday Tuesday Wednesday Thursday Friday Saturday
          1
      2  Class 

    Multivariate Distribution 31

    Convergence Concepts 40

      3
      4

      5 

      6

      7 Class  Summary

    Sums of Random Variables from a Random Sample 32 & 33

      8

      9  Class 

    Properties of the sample mean and variance 34 & 35

     

    10
    11

    12

    13

    14 Class

    Order Statistics and Convergence Concepts 37 & 38

    15

    16 Class

    Generating a random sample

     

    17
    18
    19
    20

    21 Class 

     

    22

    23 Class 

     

    24
    25
    26
    27
    28 Class 
    29
    30 Class 
    31

    January 2006


     Sunday Monday Tuesday Wednesday Thursday Friday Saturday

     1

     2 3 4
    Class  Summary

     

      5
      6

    Class  Review

    上課最後一天

      7
      8

      9

      10
     11 期末考
     12
     13
    14
    15

    16 寒假開始

    17
    18

     

    19
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    22
    23
    24
    25
    26
    27
    28 除夕
    29
    30
    31        

    Some useful website:

    1.  Optimization (convex and constrained optimization) See Lecture Notes 1, 2, 3, 10    

         at http://www.princeton.edu/~chiangm/class.html.

    2.  Linear algebra: Professor Strang's Class 18.06 Linear Algebra Lecture Videos, Fall 1999

    Software

     

     



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