READING AND HOMEWORK ASSIGNMENTS FOR STOR 755, SPRING 2009
Assignment 0.
Look over Chapter 1 in Shao and read Chapter 2 in van der Vaart, with
special attention to the material on weak convergence, little and big
o notation.
Assignment 1.
Reading: Shao, Sections 5.1.1, 5.1.2 and 5.3.1
van der Vaart: Chapters 2 and 3
Homework:
1. Give a proof of the Glivenko-Cantelli in the special case that the distribution of the observations X_i is discrete.
2. Establish the relation (3) in the proof of McDiamid's inequality.
3. Indicate where and how independence is used in the proof of McDiarmid's inequality.
4. Indicate where and how independence is used in the proof of the bound on EV_n using symmetrization.
From vdV: Problems 2.4, 2.10, 2.11, 2.12, 2.18 and 2.19
Assignment 2.
Reading: van der Vaart: Chapters 4, 5, and 11.
From vdV:
Chapter 3: 1 (see Ex 3.4), 6, 7
Chapter 4: 1, 2(i)-(ii), 3
Chapter 5: 1 (use Lem 5.10), 2, 3 (typo p should be -p), 5, 7,
9 (see ex 5.37)