TMA4295 Statistical Inference

(Spring 2008)

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


Schedule:
Lectures: Monday 10:15-12:00 G21
Tuesday 14:15-16:00 F3

Exercises: Thursday 16:15-17:00 734 (SB2)


Pensum

Messages:

18.06.08: Solutions of the exam problems are here.

14.01.08: There are some changes in the schedule.

3.01.08: First lecture is 7 January, 10:15-12:00, room G21.

Plan:
Lecture 1.
(7.01.08)
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.
(8.01.08)
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.
(14.01.08)
Moment generating function. Distribution of transformations.
Chapter 2: 2.1, 2.3, 2.4.
Exercises: 1.49, 1.52, 2.12
Lecture 4.
(15.01.08)
Families of distributions.
Chapter 3: 3.1, 3.2, 3.3, 3.5.
Exercises: 2.17, 2.18
Lecture 5.
(21.01.08)
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.
(22.01.08)
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.
(28.01.08)
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.
(29.01.08)
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.
(4.02.08)
Convergence.
Chapter 5: 5.5
Exercises: 5.5, 5.15, 5.21
Lecture 10.
(5.02.08)
Point estimation.
Chapter 7: 7.1, 7.2.1
Exercises: 5.22, 5.23, 5.31
Lecture 11.
(11.02.08)
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.
(12.02.08)
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.
(18.02.08)
UMVUE
Chapter 7: 7.3.2
Exercises: 7.40, 7.41, 10.1
Lecture 14.
(19.02.08)
Sufficient statistics.
Chapter 6: 6.1, 6.2
Exercises: 6.1, 6.3, 6.6
Lecture 15.
(10.03.08)
Sufficient statistics and UMVUE.
Chapter 6: 6.2; Chapter 7: 7.3
Exercises: 6.19, 7.38
Lecture 16.
(11.03.08)
Exponential families and UMVUE.
Chapter 3: 3.4; Chapter 6: 6.2; Chapter 7: 7.3
Exercises: 7.37, 10.9b
Lecture 17.
(31.03.08)
Hypotheses testing.
Chapter 8: 8.1, 8.2, 8.3
Exercises: 6.21, 6.22
Lecture 18.
(1.04.08)
Hypotheses testing.
Chapter 8: 8.1, 8.2, 8.3
Exercises: 7.47, 8.1
Lecture 19.
(7.04.08)
Hypotheses testing.
Chapter 8: 8.1, 8.2, 8.3
Exercises: 8.13, 8.14
Lecture 20.
(8.04.08)
Hypotheses testing.
Chapter 8: 8.1, 8.2, 8.3
Exercises: 8.16, 8.18
Lecture 21.
(14.04.08)
Hypotheses testing.
Chapter 8: 8.1, 8.2, 8.3
Exercises: 8.15, 8.27
Lecture 22.
(15.04.08)
Interval estimation.
Chapter 9: 9.1, 9.2
Exercises: 8.19 (equations, arising here, are solved only numerically), 8.31
Lecture 23.
(21.04.08)
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.
(22.04.08)
Asymptotic evaluations.
Chapter 10: 10.1, 10.3, 10.4
Exercises: 9.1, 9.2
Lecture 25.
(28.04.08)
Asymptotics. Generating random samples. Bootstrap.
Chapter 5: 5.6; Chapter 10: 10.1, 10.3, 10.4
Exercises: 9.8, 9.13
Lecture 26.
(29.04.08)
Simple linear regression.
Chapter 11: 11.1, 11.3
Exercises: 10.2, 10.3
Lecture 27.
(5.05.08)
Simple linear regression.
Chapter 11: 11.3
Exercises: 11.26
Lecture 28.
(6.05.08)
Simple linear regression. Repetition
Chapter 11: 11.3
Exercises: -