Assignment 1: Due Tuesday 16 January
Reading: Ferguson, Sections 1-4
Assignment 2: Due Thursday 25 January
Reading: Ferguson, Sections 5-6
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.
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.
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)
Assignment 6: Due Tuesday 20 February
Reading: Ferguson, Sections 16-19
Problems 9.1, 9.2, 9.4, 17.1, 17.2, 17.3
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
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
Assignment 10: Due Tuesday 27 March
Assignment 11: Due Tuesday 3 April
Reading: Estimation in high dimensions: a geometric perspective, by R. Vershynin
Assignment 12: Due Tuesday 10 April
Assignment 13: Due Tuesday 17 April
Reading: Chapter 6 of M. Ledoux Lecture Notes
Assignment 14: Due Tuesday 24 April
Reading: Ch1-2 of Gaussian estimation: Sequence and wavelet models