Chapter 1, Real and Complex Analysis, Third Edition, Rudin, W., 1987.
The homework at the end of the chapter is very useful for supplemental learning for Chapter 2. Specifically problem 4 (on topology) can be done before reading Chapter 2; problems 1 (on sigma algebras and set cardinality) and 11 (on set theory, measure space, and convergent series with nonnegative terms) can be done after reading Sections 2.1 and 2.2; problems 2, 3 and 5 (all on measurable function concepts) can be done after Section 2.3.1; problems 6 (on measurable functions and integrals) and 13 (on integration of nonnegative functions) can be done after 2.3.2; and the remaining problems, 7 (on the Monotone Convergence Theorem), 8 (on Fatou’s Lemma), 9 (on Fatou’s Lemma and the Dominated Convergence Theorem), 10 (on properties of integrals and uniformly convergent sequences of functions) and 12 (on integrability and L1-space) can be done after secton 2.3.3.
Louis, T. A. (1982). Finding the observed information matrix when using the EM algorithm. Journal of the Royal Statistical Society Series B, 44:226-233.
This classic paper, which can be downloaded from JSTOR, shows how to compute variance of estimators using EM.
Homework #1--- Lecture notes pages 13-15: 1, 2, 6, 7, 11,
12, 13; Lehmann and Casella book pages 66-67: 5.6, 5.9, 5.14.
Due Tuesday, September 2, at the beginning of class. Solution to Homework #1.
Homework #2--- Lecture notes pages 39-41: 2, 3, 4, 5, 8, 9,
10, 11, 12, 19.
Remarks on Homework #2: you can answer problems 2 and 3 after studying Section
2.2.2, problem 4 after Section 2.2.3, problem 5 after Section 2.3.2, problems 8
and 9 after Section 2.4.1, problems 10 and 19 after Section 2.4.2, problem 11
after Section 2.4.3, problem 12 after Section 2.5.2.
Due Tuesday, September 16, at the beginning of class. Solution to Homework #2.
Homework #3--- Lecture notes pages 76-77: 2, 4, 5, 7;
Ferguson's book pages 11-12: 7, 8.
Remarks on Homework #3: all the problems can be done after finishing Section
3.1, expect that #7 in the lecture notes may need results from Section 3.2.
Due Tuesday, September 30, at the beginning of class. Solution to Homework #3.
Homework #4--- Lecture notes pages 76-80: 1, 11, 12, 13,
17, 18; Ferguson's book pages 42-43: 2, 3, 5; Ferguson's book page 60: 1.
Remarks on Homework #4: all the problems can done after Section 3.3 except #11
and #12 in the lecutre notes; these two can be answered after Section 3.4. I
also recommend that you consult with Ferguson's book for more information.
Due Tuesday, October 28, at the beginning of class. Solution to Homework #4.
Homework #5--- Lecture notes pages 104-107: 1,3,4,5,6,8,9;
Lehmann and Casella's book page 72: 6.35; Lehmann and Casella's book page 133:
2.21; Lehmann and Casella's book page 139: 5.22.
Remarks on Homework #5: For Problem 2.21 on page 133 in LC's book, you may
consult with Problem 6.18 on page 71 and Example 6.24 on page 43.
Due Tuesday, November 11, at the beginning of class. Solution to Homework #5.
Homework #6--- Lecture notes pages 126-129: 1,2,3,4,5,6;
Lehmann and Casella's book page 506: 4.16 (a)-(d).
Due Tuesday, November 25, at the beginning of class. Solution to Homework #6.
Dr. Emil Cornea’s office hours and location are on Monday, 11:00AM-noon, in room MHRC 3100; and on Friday, noon-1:00PM, in room MHRC 0003.
Dr. Emil Cornea has provided a proof for the formula for the density of the non-central chi square distribution presented on page 10 of the lecture notes. Recall in this case that the scale parameter for the gamma density is the reciprocal of the usual parameter. Dr. Cornea’s Proof.
The midterm will be on Tuesday, October 7. The class time on Thursday, October 2, will be devoted to review for the midterm: please come to class that day prepared with 2-3 meaningful questions to ask regarding material covered on the midterm. The content for the exam covers Chapter 1, Chapter 2, and Section 3.1 of Chapter 3 in the lecture notes. Sample practice exams and some practice problems can be downloaded:
Sample Exam I with its solution, Sample Exam II with its solution, Sample Exam III with its solution, and Practice Problems with its solution.
Midterm self-critiques will be due on Tuesday, October 21. The idea is to accurately clarify all of the errors that were made on the midterm. What you turn in needs to be easy for the grader to follow. Up to a half of the points lost on the midterm can be added back to the original score. The exam and solution set for the 2008 midterm are here: exam and solution.
The final exam will be on Thursday, December 11, from 4:00-7:00PM in room 0003-4 MHRC. The final exam covers all of Chapter 3, Chapter 4 and Chapter 5. The class time on Tuesday, December 2, will be devoted to review for the final: please come to class that day prepared with 2-3 meaningful questions to ask regarding the material covered on the final. Some practice exams for the final exam can be downloaded:
Practice 1 (Solution), Practice 2 (Solution), Practice 3 (Solution), and Practice 4 (Solution).