STA 7334: Assignments

AS = Asymptotic Statistics by A. W. van der Vaart

Assignment 1 (Due Friday, Sep 24, by Noon)

Do exercises 2.3, 2.4, and 2.5 of the course notes, plus exercises 2.16 and 2.17 of AS. In case the numbers change, here is a copy of the exercises at the time this assignment was made.

Assignment 2 (Due Friday, Oct 1, by Noon)

Exercises 2.12, 3.1, 3.4, and 3.8 of AS.
Note: the second part of AS 3.8, concerning the expectation of 1/|Xbar|, is false as stated for n = 1. It is true for n > 1, but is still somewhat difficult to prove. To make things easier, rather than assuming that the density f is bounded and strictly positive in a neighborhood of zero, assume that f is bounded away from zero in a neighborhood of zero, i.e., that there exists an eta > 0 and a delta > 0 such that f(x) > eta for all x with absolute value less than delta (this would be true for example if f was positive and continuous at zero). With these hypotheses E(1/|Xbar|) is infinite for all n >= 1.

Assignment 3 (Due Friday, Oct 29, by Noon)

Do exercise 5.13 of AS.

Assignment 4 (Due Tuesday, Nov 16)

Do exercises 5.1 and 5.2 of AS.

Assignment 5 (Due by noon, Tuesday, Dec 14)

Do this problem.

Additional Suggested Problems

AS, Chapter 2: You should be able to do all of the unassigned problems at the end of Chapter 2. Most of them are review problems for the probability course, and the majority are straightforward.
AS, Chapter 3: Again, you should be able to do most or all of the unassigned problems at the end of Chapter 2.
AS, Chapter 4: Exercises 1 and 3 are pretty simple and you should be able to do them. Exercises 2, 4, and 5 are specifically about exponential families, which we may return to later. Exercise 6 is more of an analysis question that bears on uniqueness of the method of moments estimator.
AS, Chapter 5: Exercises 4, 5, 6, 9, 10, 18 are routine examples and you should be able to do them. Exercises 9, 17, and 19 are standard counterexamples that everyone should know how to do. You should do exercises 5.7 and 5.8 to make sure you understand things.
AS, Chapter 12: Exercises 1, 6, 7, 9, 10, 11.



Home Courses Research Downloads Useful Links Amusements Gripes Brett Presnell Associate Professor 225 Griffin-Floyd Hall (352) 392 1941 FAX: (352) 392 5175 presnell@stat.ufl.edu Office Hours MWF: 3:00–4:30 pm	STA 7334: Assignments AS = Asymptotic Statistics by A. W. van der Vaart Assignment 1 (Due Friday, Sep 24, by Noon) Do exercises 2.3, 2.4, and 2.5 of the course notes, plus exercises 2.16 and 2.17 of AS. In case the numbers change, here is a copy of the exercises at the time this assignment was made. Assignment 2 (Due Friday, Oct 1, by Noon) Exercises 2.12, 3.1, 3.4, and 3.8 of AS. Note: the second part of AS 3.8, concerning the expectation of 1/\|Xbar\|, is false as stated for n = 1. It is true for n > 1, but is still somewhat difficult to prove. To make things easier, rather than assuming that the density f is bounded and strictly positive in a neighborhood of zero, assume that f is bounded away from zero in a neighborhood of zero, i.e., that there exists an eta > 0 and a delta > 0 such that f(x) > eta for all x with absolute value less than delta (this would be true for example if f was positive and continuous at zero). With these hypotheses E(1/\|Xbar\|) is infinite for all n >= 1. Assignment 3 (Due Friday, Oct 29, by Noon) Do exercise 5.13 of AS. Assignment 4 (Due Tuesday, Nov 16) Do exercises 5.1 and 5.2 of AS. Assignment 5 (Due by noon, Tuesday, Dec 14) Do this problem. Additional Suggested Problems AS, Chapter 2 You should be able to do all of the unassigned problems at the end of Chapter 2. Most of them are review problems for the probability course, and the majority are straightforward. AS, Chapter 3 Again, you should be able to do most or all of the unassigned problems at the end of Chapter 2. AS, Chapter 4 Exercises 1 and 3 are pretty simple and you should be able to do them. Exercises 2, 4, and 5 are specifically about exponential families, which we may return to later. Exercise 6 is more of an analysis question that bears on uniqueness of the method of moments estimator. AS, Chapter 5 Exercises 4, 5, 6, 9, 10, 18 are routine examples and you should be able to do them. Exercises 9, 17, and 19 are standard counterexamples that everyone should know how to do. You should do exercises 5.7 and 5.8 to make sure you understand things. AS, Chapter 12 Exercises 1, 6, 7, 9, 10, 11.