TMA4295 Statistical Inference

(Spring 2009)



Messages:

26.05.09: Here are the solutions to the exam problems.

15.05.09: Here is the list of topics for the exam.

08.05.09: Friday next week (May 15), I shall give you a list of topics that you should focus on for the exam (May 26).

30.04.09: Links to earlier exam problems are now available. The allowed aids at the exam are according to code C, which agrees with what I have said (yellow stamped A5 ...).  NOTE! No lectures next week.

09.03.09: The TA will be attending a workshop next week, so the exercise class will be cancelled.

26.01.09: A tentative curriculum has been posted.

14.01.09: NOTE! The lecture on Tuesdays has been moved to B22, and it now starts at 10:15.

12.01.09: First lecture is 13 January, 11:15-13:00, room F2


Textbook:   
George Casella, Roger L. Berger. Statistical Inference, 2002, Duxbury.

Lecturer:  
Professor Arvid Naess.  Office: 1144, S1.  Email: arvidn@math.ntnu.no

TA:   
Gabriele Martinelli, Email: gabriele@math.ntnu.no

Schedule:

Lectures: Monday 8:15-10:00 F2
Tuesday 10:15-12:00 B22


Exercises: Thursday 14:15-15:00 F2


Curriculum
Earlier exam problems

Plan:
Lecture 1.
(13.01.09)
Probability theory.
Chapter 1: 1.1, 1.2, 1.3
Exercises: 1.1, 1.2, 1.4, 1.9, 1.11, 1.13
Lecture 2.
(19.01.09)
Probability theory. Expectations and moments.
Chapter 1: 1.4, 1.5, 1.6. Chapter 2: 2.2, 2.3.
Exercises: 1.33, 1.38, 1.39
Lecture 3.
(20.01.09)
Moment generating function. Distribution of transformations.
Chapter 2: 2.1, 2.3, 2.4.
Exercises: 1.49, 1.52, 2.12
Lecture 4.
(26.01.09)
Families of distributions.
Chapter 3: 3.1, 3.2, 3.3, 3.5.
Exercises: 2.17, 2.18
Lecture 5.
(27.01.09
Multiple random variables.
Chapter 4: 4.1, 4.2, 4.3 (something), 4.4 (something), 4.6 (something)
Exercises: 2.1, 2.19, 2.20, 2.25, 2.31
Lecture 6.
(02.02.09)
Conditional distributions.
Chapter 4: 4.2, 4.4 (Theorems 4.4.3, 4.4.7)
Exercises: 2.15, 3.21, 3.23, 3.25
Lecture 7.
(03.02.09)
Covariance and correlation. Inequalities.
Chapter 3: 3.6 (Theorem 3.6.1); Chapter 4: 4.5, 4.7 (Theorems 4.7.3, 4.7.7)
Exercises: 4.1, 4.2, 4.6, 4.13
Lecture 8.
(09.02.09)
Basic concepts of statistics. Sums. Convergence.
Chapter 5: 5.1, 5.2, 5.5
Exercises: 4.41, 4.42, 4.43, 4.58, 4.63
Lecture 9.
(10.02.09)
Convergence.
Chapter 5: 5.5
Exercises: 5.5, 5.15, 5.21
Lecture 10.
(16.02.09)
Point estimation.
Chapter 7: 7.1, 7.2.1
Exercises: 5.22, 5.23, 5.31
Lecture 11.
(17.02.09)
MME and MLE. Evaluation of estimators.
Chapter 7: 7.1, 7.2.1, 7.2.2, 7.3.1; Chapter 10: 10.1.1
Exercises: 7.1, 7.2a, 7.6b,c
Lecture 12.
(23.02.09)
Evaluation of estimators.
Chapter 7: 7.1, 7.2.1, 7.2.2, 7.3.1; Chapter 10: 10.1.1
Exercises: 7.7, 7.8, 7.11 (in (a) only find the MLE)
Lecture 13.
(24.02.09)
UMVUE
Chapter 7: 7.3.2
Exercises: 7.40, 7.41, 10.1
Lecture 14.
(02.03.09)
Sufficient statistics.
Chapter 6: 6.1, 6.2
Exercises: 6.1, 6.3, 6.6
Lecture 15.
(03.03.09)
Sufficient statistics and UMVUE.
Chapter 6: 6.2; Chapter 7: 7.3
Exercises: 6.19, 7.38
Lecture 16.
(09.03.09)
Exponential families and UMVUE.
Chapter 3: 3.4; Chapter 6: 6.2; Chapter 7: 7.3
Exercises: 7.37, 10.9b
Lecture 17.
(10.03.09)
Hypotheses testing.
Chapter 8: 8.1, 8.2, 8.3
Exercises: 6.21, 6.22
Lecture 18.
(16.03.09)
Hypotheses testing.
Chapter 8: 8.1, 8.2, 8.3
Exercises: 7.47, 8.1
Lecture 19.
(17.03.09)
Hypotheses testing.
Chapter 8: 8.1, 8.2, 8.3
Exercises: 8.13, 8.14
Lecture 20.
()
Hypotheses testing.
Chapter 8: 8.1, 8.2, 8.3
Exercises: 8.16, 8.18
Lecture 21.
()
Hypotheses testing.
Chapter 8: 8.1, 8.2, 8.3
Exercises: 8.15, 8.27
Lecture 22.
()
Interval estimation.
Chapter 9: 9.1, 9.2
Exercises: 8.19 (equations, arising here, are solved only numerically), 8.31
Lecture 23.
()
Interval estimation. Asymptotic evaluations.
Chapter 9: 9.1, 9.2.1, 9.2.2, 9.3.1; Chapter 5: 5.5.4; Chapter 10: 10.1, 10.3, 10.4
Exercises: 8.23, 8.45
Lecture 24.
()
Asymptotic evaluations.
Chapter 10: 10.1, 10.3, 10.4
Exercises: 9.1, 9.2
Lecture 25.
()
Asymptotics. Generating random samples. Bootstrap.
Chapter 5: 5.6; Chapter 10: 10.1, 10.3, 10.4
Exercises: 9.8, 9.13
Lecture 26.
()
Simple linear regression.
Chapter 11: 11.1, 11.3
Exercises: 10.2, 10.3
Lecture 27.
()
Simple linear regression.
Chapter 11: 11.3
Exercises: 11.26
Lecture 28.
()
Simple linear regression. Repetition
Chapter 11: 11.3
Exercises: -