# Fundamentals of Modern Statistical Inference

Fundamentals of Modern Statistical Inference All relevant materials will be available in due course on this page.

Time: 9-12 Fridays. Venue: MB 2.24.

Marks are not negotiable. I do not reply to questions in any form about marks.

Contents

1. Chapter 1: An overview of statistical inference: through a linear regression model

2. Model introduction (Week 1)

3. The least squares estimator and the maximum likelihood estimator (Week 1)

4. Data reduction: the sufficiency principle and the likelihood principle (Week 1)

5. Confidence intervals and hypothesis testing (Week 2)

6. Asymptotics (Week 2)

7. Beyond independence (Week 2)

8. Chapter 2: Central limit theorems

9. A statement on i.i.d. cases (Week 3)

10. Proof 1: The Fourier method (Week 3)

11. Proof 2: The Moment method (Week 3)

12. Proof 3: The Lindeberg method (Week 4)

13. Chapter 3: Stein's method for normal approximation

14. Introduction (Week 4)

15. Characterisation (Week 5)

16. Construction of the Stein identities (Week 5)

17. Normal approximations: Independent random variables (Week 5)

18. Normal approximations: Locally dependent random variables (Week 6)

19. Normal approximations: Exchangeable pairs (Week 6)

20. Chapter 4: The minimax theory

21. Introduction and general scheme (Week 7)

22. Le Cam's method (Week 7)

23. Fano's method (Week 8)

24. Tsybakov's bound (Week 8)

25. The Varshamov--Gilbert theorem (Week 8)

26. Minimax classification (Week 9)

27. Minimax hypothesis testing (Week 9)

Lecture notes

1. Chapters 1 and 2 [pdf]

2. Chapter 3. Sections 1, 2.1, 2.3, 3.1 and 3.3 of this.

3. Chapter 4. Sections 1, 2, 3, 4, 5, 6, 7, 8, 9.3 and 11 of this.

Assignments

There will be two sets of assignments in total. Submit by due dates on Moodle.

1. Assignment 1, due date: 19 Nov 2021. [pdf]

2. Assignment 2, due date: 17 Dec 2021. [pdf]

Exam

References

1. [Chapter 1 Ref] Casella, G. and Berger, R. L. (2021). Statistical inference. Cengage Learning.

2. [Chapter 1 Ref] Previous lecture notes. [pdf]

3. [Chapter 2 Ref] Some lecture notes by Terrence Tao [link]

4. [Chapter 3 Ref] Chen, L. H., Goldstein, L., and Shao, Q. M. (2011). Normal approximation by Stein's method (Vol. 2). Heidelberg: Springer.

5. [Chapter 4 Ref] Tsybakov, Alexandre B. (2009). Introduction to Nonparametric Estimation. Springer.

Office hour

I hold office hours 12-1pm on Wednesdays and 1-2pm on Fridays. Please book a slot in advance by sending me an email.