MA8701 General Statistical Methods

(Spring 2007)

Textbook:   Peter J. Bickel and Kjell A. Doksum. Mathematical statistics: basic ideas and selected topics, 2-nd edition, 2001, Prentice Hall.


Messages:

30.01.07: Our meeting on Monday, 5.01.07 (13:15), is in room 922 (SB2).

29.01.07: Plan of MA8701 in 2005 is here

9.01.07: Our meetings are on Tuesdays, 12:30, room 822 (SB2).

3.01.07: First meeting is 9 January, 13:00, room 822 (SB2). If this time is not convenient, please let me know.


Plan:
2-3 weeks Statistical models. Parametrization. Identifiability. Regular models. Statistics. Bayesian models. Conjugate families. Basic concepts of the decision theory: decision, loss function, decision rule, risk. Comparison of decision rules. Classical criterion. Bayes criterion. Minimax criterion. Admissibility.
Chapter 1: 1.1, 1.2, 1.3
Exercises: 1.1.3, 1.1.6
3-4 weeks Theory: the same.
Chapter 1: 1.1, 1.2, 1.3
Exercises: 1.1.11, 1.2.2, 1.2.6, 1.2.11, 1.3.14, 1.3.15
4-6 weeks Prediction. Sufficient statistics. Exponential families.
Chapter 1: 1.4, 1.5, 1.6.1, 1.6.2, 1.6.4, 1.6.5
Exercises: 1.5.3, 1.5.7, 1.5.9
6-7 weeks Theory: the same.
Chapter 1: 1.4, 1.5, 1.6.1, 1.6.2, 1.6.4, 1.6.5
Exercises: 1.4.5, 1.4.6, 1.5.15, 1.6.1, 1.6.2, 1.6.4 (a-c), 1.6.5, 1.6.7, 1.6.11 (b,c)
7-8 weeks Methods of estimation.
Chapter 2: 2.1, 2.2
Exercises: 2.1.3, 2.1.6, 2.1.9
8-9 weeks Maximum likelihood in exponential families.
Chapter 2: 2.3
Exercises: 2.2.1, 2.2.10, 2.2.13
9-10 weeks Measures of performance.
Chapter 3: 3.1, 3.2, 3.3
Exercises: 3.2.1, 3.2.2
10-11 weeks UMVUE. Other criteria.
Chapter 3: 3.4, 3.5
Exercises: 3.4.1, 3.4.5a, 3.4.10, 3.4.12a
11-12 weeks Hypotheses testing.
Chapter 4: 4.1, 4.2, 4.3
Exercises: 4.1.1, 4.2.4a, 4.3.5
12-13 weeks Confidence regions. Pivots. Inverting a test statistic.
Chapter 4: 4.4, 4.5
Exercises: 4.4.2, 4.4.5, 4.4.12, 4.5.2
13, 15 weeks Bayesian set estimation. Prediction intervals. Likelihood ratio procedures.
Chapter 4: 4.7, 4.8, 4.9
Exercises: 4.7.2, 4.9.8
16-17 weeks Convergence. Asymptotics.
Appendix A: A14, A15; Appendix B: B7; Chapter 5: 5.1, 5.2
Exercises: 5.1.3, 5.1.4
18-19 weeks Asymptotics.
Chapter 5: 5.3.1, 5.3.2 (up to Monte Carlo Simulation), 5.3.3, 5.4.3; Chapter 6: 6.2.2
Exercises: 5.2.2