STOR 655 Homework, Spring 2018

Assignment 1: Due Tuesday 16 January

Reading: Ferguson, Sections 1-4

Problems

 

Assignment 2: Due Thursday 25 January

Reading: Ferguson, Sections 5-6

Problems

 

Assignment 3: Due Tuesday 29 January

Reading: Ferguson, Sections 5-7

Problem 1.1 (first part only), 1.2, 1.3, and 1.4.

Problem 4.1. First carefully evaluate the expected value of beta-hat and alpha-hat. It follows from this that the relevant quantity to consider in parts a,b of the question is the variance of the the estimates. Recall that converence in quadratic mean (qm) is equivalent to L_2 convergence.

Problem 4.3. Write out your argument carefully, and show details.

Problems

 

Assignment 4: Due Tuesday 6 February

Reading: Ferguson, Sections 6-10

Problems 2.6, 3.1, 5.1, 5.7 (use the Lindebergh CLT), 6.1 parts a and c (establish Theorem 6′ (a) under the assumption that f is continuous everywhere), 6.4, 6.5.

Problems

 

Assignment 5: Due Tuesday 13 February

Reading: Ferguson, Sections 8-10, 16-17

Problems 6.5, 7.1, 7.2, 7.3a, 7.4, 8.3, 8.4 (see solutions)

Problems

 

Assignment 6: Due Tuesday 20 February

Reading: Ferguson, Sections 16-19

Problems 9.1, 9.2, 9.4, 17.1, 17.2, 17.3

Problems

 

Assignment 7: Due Tuesday 27 April

Reading: Ferguson, Sections 16-20, 22

Problems 18.1a, 18.2, 18.3, 18.4, 19.1, 19.3 (the question assumes that the nuisance parameters are *unknown*; also answer parts (a) and (b) in case the nuisance parameters are *known*), 19.5

Problems

 

Assignment 8: Due Friday 2 March by 4pm in TA Leo Yufeng Liu’s mailbox

Read Ferguson, Sections 16-20, 22.

Problems 20.1a, 20.3, 22.2, 22.3

 

Assignment 9: Due Tuesday 20 March

Problems

 

Assignment 10: Due Tuesday 27 March

Problems

 

Assignment 11: Due Tuesday 3 April

Reading: Estimation in high dimensions: a geometric perspective, by R. Vershynin

Problems

 

Assignment 12: Due Tuesday 10 April

Gaussian Comparison Lemma

Problems

 

Assignment 13: Due Tuesday 17 April

Reading: Chapter 6 of M. Ledoux Lecture Notes

Problems

 

Assignment 14: Due Tuesday 24 April

Reading: Ch1-2 of Gaussian estimation: Sequence and wavelet models

Problems