Main textbooks
Cox and Hinkley (1976) Theoretical Statistics. Chapman and Hall/CRC.
Davison (2003) Statistical Models. Cambridge University Press.
This course focuses on hypothesis testing, which includes classical significance tests and modern selective inference methods. The main emphasis is on understanding general concepts rather than emphasizing mathematical rigour.
COX AND HINKLEY (1976)
§3 PURE SIGNIFICANCE TESTS
§3.1 Null hypotheses
§3.2 Test
statistics and their null distributions
§3.3 Composite null
hypotheses
§3.4 Discussion
Examples 3.1, 3.2, 3.4
Exercises 3.1, 3.13
§6 DISTRIBUTION-FREE AND RANDOMIZATION TESTS
§6.1 General
§6.4 Randomization tests
Example 6.7
Exercise 6.3
§7 INTERVAL ESTIMATION
§7.1 Introduction
§7.2 Scalar
parameter
Examples 7.1, 7.4
Exercise 7.1
DAVISON (2003)
Section 7.3.1 (pages 325 -
332)
Section 7.3.4 (pages 343 - 346)
Exercises 7.3 (page
347): 1, 2, 3
Problems 7.5 (page 350 - 351): 15, 16, 17, 18
COX AND HINKLEY (1976)
§4 SIGNIFICANCE TESTS: SIMPLE NULL HYPOTHESES
§4.1 General
§4.2 Formulation
§4.3 Simple null hypothesis and simple alternative
hypothesis
§4.4 Some examples
§4.5 Discrete problems
§4.6
Composite alternatives
§4.7 Two-sided tests
§4.8 Local power
§4.9 Multidimensional alternatives
Examples 4.1, 4.3, 4.4, 4.5, 4.9,
4.10, 4.11, 4.13
Exercises 4.6, 4.13
§5 SIGNIFICANCE TESTS: COMPOSITE NULL HYPOTHESES
§5.1 General
§5.2 Similar regions
§5.3 Invariant tests
§5.4 Some more
difficult problems
Examples 5.1, 5.2, 5.5, 5.9, 5.10
§7 INTERVAL ESTIMATION
§7.3 Scalar parameter with nuisance
parameters
§7.4 Vector parameter
§7.5 Estimation of future
observations
DAVISON (2003)
Section 7.3.2 (pages 333 -
339)
Section 7.3.3 (pages 339 - 343)
Exercises 7.3 (page
347): 4, 5, 6, 7, 8, 9, 13, 14
Problems 7.5 (page 350 - 351): 19,
20
All of the course material is on the github repo.
Written.
For the preparation of the written exam, you are expected to study all the material (books, lecture notes, slides) including proofs, and complete all the examples and exercises.
Cox and Hinkley (1976) Theoretical Statistics. Chapman and Hall/CRC.
Davison (2003) Statistical Models. Cambridge University Press.
Casella and Berger (2002) Statistical inference. Duxbury Press.
Cox (2006) Principles of Statistical Inference. Cambridge University Press.
Lehmann and Romano (2005) Testing Statistical Hypotheses. Springer Texts in Statistics.
| N | Date | Hours | Room | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | April 15, 2024 | 10-12 and 14-16 (4 hrs) | Aula Seminari U7-2104 | |||||||||
| 2 | April 18, 2024 | 9-12 (3 hrs) | Zoom (remote) | |||||||||
| 3 | April 22, 2024 | 10-12 and 14-16 (4 hrs) | Aula Seminari U7-2104 | |||||||||
| 4 | April 29, 2024 | 10-12 (2 hrs) | Zoom (remote) | |||||||||
| 5 | May 7, 2024 | 10-12 (2 hrs) | Zoom (remote) |