MASC02 Inference Theory, 2nd course

Department of Mathematical Statistics
Lund University with Lund Institute of Technology

Current information for spring semester 2010.

Introductory meeting: March 24, 2010 at 13.15-15.00 in MH 309A.
Course schedule: The course consists of two lectures and one exercise session per week.
Lectures are on Mondays 8.15-10.00 and Wednesdays 13.15-15.00.
Exercises are on Wednesdays 10.15-12.00.
Credits: 7.5 ECTS credits (5 points)
Lecturer: Dragi Anevski
e-mail: dragi@maths.lth.se
Course material: The course follows the two books:: E.L. Lehman, G. Casella, Theory of Point Estimation, Springer 1998.
E.L. Lehman, J.P. Romano, Testing Statistical Hypothesis, Springer 2005.
Only parts of the material in the books will be covered. Both books are nevertheless recommended bying, as they are excellent reference litterature. (Both books are available as E-books free of charge via Elin at the LU Library). The course will begiven in English upon request, otherwise in Swedish. Lecture notes will be posted after each lecture on this page.

The background material is treated in Casella and Lehmann chapters 1.2-1.3; students that feel uncertain on whether they have sufficient backgroud should consult these pages. More detailed background information on measure theory and topology can be found here.
Detailed schedule of lectures

Lecture Date and Place Content Material

1 24/3, MH309A Overview. The inference problem. Group families. Casella and Lehmann 1.1, 1.4-1.5. Lecture 1.

2 29/3, MH227 Group families and exponential families. Casella and Lehmann 1.4-1.5. Lecture 2.

3 31/3, MH227 Group families and exponential families. Casella and Lehmann 1.4-1.5.

4 7/4, MH309A Exponential families. Sufficiency. Casella and Lehmann 1.5-1.6.

5 12/4, MH309A Sufficiency. Casella and Lehmann 1.6.

6 19/4, MH227 Convex loss functions. UMVU estimation. Casella and Lehmann 1.7, 2.1.

7 21/4, MH227 UMVU estimation. Casella and Lehmann 2.1.

8 26/4, MH227 UMVU estimation. Continuous and discrete problems. Casella and Lehmann 2.2, 2.3

9 28/4, MH227 UMVU estimation. Discrete problems. Equivariance Casella and Lehmann 2.3, 3.2, 3.1 Lecture 9

10 3/5, MH227 Location and location/scale equivariance Casella and Lehmann 3.1, 3.3 Lecture 10

11 10/5, MH227 Location and location/scale equivariance Casella and Lehmann 3.3 Lecture 11

12 12/5, MH227 Location/scale equivariance, average risk optimality (Bayesian inference). Casella and Lehmann 3.3, 4.1.

13 17/5, MH227 Average risk optimality (Bayesian inference). Casella and Lehmann 4.1.

14 19/5, MH227 Bayesian inference, single prior Bayes. Casella and Lehmann 4.1-4.2.

15 24/5, MH227 Minimax estimation Casella and Lehmann 5.

16 26/5, 10-12, MH227 Decision theory Lehmann and Romano 1.2, 1.4, 1.6, 1.8. Lecture 16,17

17 26/5, 13-15, MH227 Decision Theory Lehmann and Romano 1.2, 1.4, 1.6, 1.8, 2. Lecture 16,17

18 31/5, MH227 Neyman-Pearsons lemma. p-values. Monotone LR. Lehmann and Romano 3.1, 3.2, 3.3

19 2/6, 10-12, MH227 Monotone LR. Lehmann and Romano 3.4

20 2/6, 13-15, MH227 Decision Theory Lehmann and Romano Lecture 18-20


Exercises

Exercise Date and Place Theory Exercise number

1 7/4, MH309A The inference problem. Group families. 1.2, 1.10, 4.1, 4.13, 4.14
2 14/4, MH227 Exponential families, sufficiency. 5.1, 5.10(a-e), 5.12, 5.13, 4.5 (what is the conclusion of this result?)

3 12/5, MH227 Sufficiency and convex loss functions. UMVU estimation 6.1, 6.2, 6.5, 6.6, 6.16, 2.1.12, 2.1.2

4 19/5, MH227 UMVU estimation 2.1.15, 2.1.18, 2.2.1, 2.3.2, 2.3.4, 2.3.6, 2.3.18, 2.3.25


Last modified: April 30 15:00:00 CET 2010

Lecture	Date and Place	Content	Material
1	24/3, MH309A	Overview. The inference problem. Group families.	Casella and Lehmann 1.1, 1.4-1.5. Lecture 1.
2	29/3, MH227	Group families and exponential families.	Casella and Lehmann 1.4-1.5. Lecture 2.
3	31/3, MH227	Group families and exponential families.	Casella and Lehmann 1.4-1.5.
4	7/4, MH309A	Exponential families. Sufficiency.	Casella and Lehmann 1.5-1.6.
5	12/4, MH309A	Sufficiency.	Casella and Lehmann 1.6.
6	19/4, MH227	Convex loss functions. UMVU estimation.	Casella and Lehmann 1.7, 2.1.
7	21/4, MH227	UMVU estimation.	Casella and Lehmann 2.1.
8	26/4, MH227	UMVU estimation. Continuous and discrete problems.	Casella and Lehmann 2.2, 2.3
9	28/4, MH227	UMVU estimation. Discrete problems. Equivariance	Casella and Lehmann 2.3, 3.2, 3.1 Lecture 9
10	3/5, MH227	Location and location/scale equivariance	Casella and Lehmann 3.1, 3.3 Lecture 10
11	10/5, MH227	Location and location/scale equivariance	Casella and Lehmann 3.3 Lecture 11
12	12/5, MH227	Location/scale equivariance, average risk optimality (Bayesian inference).	Casella and Lehmann 3.3, 4.1.
13	17/5, MH227	Average risk optimality (Bayesian inference).	Casella and Lehmann 4.1.
14	19/5, MH227	Bayesian inference, single prior Bayes.	Casella and Lehmann 4.1-4.2.
15	24/5, MH227	Minimax estimation	Casella and Lehmann 5.
16	26/5, 10-12, MH227	Decision theory	Lehmann and Romano 1.2, 1.4, 1.6, 1.8. Lecture 16,17
17	26/5, 13-15, MH227	Decision Theory	Lehmann and Romano 1.2, 1.4, 1.6, 1.8, 2. Lecture 16,17
18	31/5, MH227	Neyman-Pearsons lemma. p-values. Monotone LR.	Lehmann and Romano 3.1, 3.2, 3.3
19	2/6, 10-12, MH227	Monotone LR.	Lehmann and Romano 3.4
20	2/6, 13-15, MH227	Decision Theory	Lehmann and Romano Lecture 18-20

Exercise	Date and Place	Theory	Exercise number
1	7/4, MH309A	The inference problem. Group families.	1.2, 1.10, 4.1, 4.13, 4.14
2	14/4, MH227	Exponential families, sufficiency.	5.1, 5.10(a-e), 5.12, 5.13, 4.5 (what is the conclusion of this result?)
3	12/5, MH227	Sufficiency and convex loss functions. UMVU estimation	6.1, 6.2, 6.5, 6.6, 6.16, 2.1.12, 2.1.2
4	19/5, MH227	UMVU estimation	2.1.15, 2.1.18, 2.2.1, 2.3.2, 2.3.4, 2.3.6, 2.3.18, 2.3.25