STAT 549-001: Functional Data Analysis and Wavelets

Wavelets in Statistics and their Applications

Marina Vannucci

Spring 2008

Homework Assignments

• 1. - Due Jan. 22nd - Read Chapter 1(Introduction).
  Write some relatively brief comments about the chapter that at least touch on the following four questions:
  1. Is the chapter of value to readers of the book, why or why not?
  2. What did you like, if anything, about the chapter?
  3. What did you dislike, if anything, about the chapter?
  4. What changes, if any, would you like to see in the chapter?

• 2. - Due Jan. 29nd - Read Chapter 2(Orthogonal Wavelet Bases) up to Section 2.5 (included).
  Write some relatively brief comments about the chapter that at least touch on the following four questions
  (comments on specific sections will be helpful):
  1. Is the chapter of value to readers of the book, why or why not?
  2. What did you like, if anything, about the chapter?
  3. What did you dislike, if anything, about the chapter?
  4. What changes, if any, would you like to see in the chapter?

• 3. - Due Feb. 5th - Finish reading Chapter 2(Orthogonal Wavelet Bases) (Section 2.6 and appendix on convergence properties)
  and read Appendix of book (Functional Spaces).
  3a) Write some relatively brief comments about the appendix of the chapter.
  Is it of value to readers of the book, why or why not?
  What changes, if any, would you like to see?
  3b) Was the Appendix on functional spaces useful? What would you like to change or add to it, if any?
  3c) Work on the Problems at the end of Chapter 2.

• 4. - Due Feb. 12th - Read Chapter 3(Discrete Wavelet Transforms)
  4a) Write some relatively brief comments about the Chapter.
  1. Is the chapter of value to readers of the book, why or why not?
  2. What did you like, if anything, about the chapter?
  3. What did you dislike, if anything, about the chapter?
  4. What changes, if any, would you like to see in the chapter?
  4b) Using the Matlab wavelet toolbox, re-create Figure 3.10. Write me the code you use, and an explanation of how you made the plot. Make the plot first using Haar wavelets and then Daubechies N=7 wavelets.
  4c) OPTIONAL: Work on the Problems at the end of the Chapter.

• 5. - Due Feb. 19th - Read Chapter 4(Density Estimation), excluding Section 4.6 (this will not be covered in class)
  5a) Write some relatively brief comments about the Chapter.
  1. Is the chapter of value to readers of the book, why or why not?
  2. What did you like, if anything, about the chapter?
  3. What did you dislike, if anything, about the chapter?
  4. What changes, if any, would you like to see in the chapter?
  5b) Using the Matlab wavelet toolbox, write a code to implement the simple linear estimator (4.6). Use a simulated density of your choice. Write me the code you use (pay attention to section 4.4.3 - things are easier with data rescaled in [0,1]). Use Haar wavelets and Daubechies N=7.

• 6. - Due March 11th -
  1) Install WaveLab on your computer.
  2) Using WaveLab download an image and plot its MRA decomposition (hint: use MakeImage and FWT2_PO)
  3) Using WaveLab recreate this plot (You can use any signal you like). Hint: use MakeSignal and ThreshWave
  4) Work on the Problems at the end of Chapter 4 (Density).

• 7. - Due March 30th -Read Chapter 6(Functional Data)
  7a) Write some relatively brief comments about the Chapter.
  1. Is the chapter of value to readers of the book, why or why not?
  2. What did you like, if anything, about the chapter?
  3. What did you dislike, if anything, about the chapter?
  4. What changes, if any, would you like to see in the chapter?
  7b) Using the software GaussianWaveDen recreate (even partially) one of the simulation studies of Antoniadis et al. (2001) paper "Wavelet estimators in ....".
  

• 8. - Due April 14th -Read Chapter 8(Stochastic Processes)
  8a) Write some relatively brief comments about the Chapter.
  1. Is the chapter of value to readers of the book, why or why not?
  2. What did you like, if anything, about the chapter?
  3. What did you dislike, if anything, about the chapter?
  4. What changes, if any, would you like to see in the chapter?
  8b) Go back to the order and outline of the STAT chapters of the book (see webpage 'papers'). Would you like to see a different order ot the topics?
  8c) Now read the preface of the book. Please comment on that.
  8d) Finally, re-examine Appendices A and B. Anything you would like to add/delete from there?