Stat 6520: Nonparametric Density Estimation and Smoothing

Instructor: Michael Minnotte
Office: Lund 201-C
Phone: 797-2844 (office)
E-mail: minnotte@math.usu.edu
Office Hours: TBA

Nonparametric density estimation and nonparametric regression are powerful tools for exploratory data analysis, and allow us to gain greater understanding of our data and the populations they represent without requiring perhaps unjustified assumptions as to the distributional forms of that data. This course will examine theoretical, applied, and implementational issues in a variety of methods. Key techniques will include histograms, frequency polygons, and estimates using splines, kernels, and wavelets. Implementation, efficiency, and applications in one, two, and high dimensions wil be discussed.

Prerequisites: A good foundation in probability through expectation and variance of continuous random variables, such as Math 5710 or equivalent, will make things much easier. You may take this concurrently with 5710, but come talk to me if this is necessary.

Assignments: There will be a brief homework assignment every week. Additionally, there will be several projects during the quarter. These will generally require some computer work and a write-up, and may be done in small groups of two or three. Finally, each student will also be expected to individually produce a written and oral report on a related topic of his or her choosing during the last two weeks of class. Assignments will be handed out in class and posted to the web site.

Grades: Each assignment will include a value in points. Most homeworks will be 10 points, and the projects and reports will generally be around 50 points. Your final grade will be determined by the sum of your points in all assignments.

Text: Simonoff, Jeffrey S., (1996), Smoothing Methods in Statistics, Springer-Verlag.

Software: You may use either S-Plus or R. S-Plus is available on the Math and Stat Department's Unix system (talk to me if you need an account). R is a Gnu-license (freeware) clone of S-Plus, and is available for free download (Windows and Unix) from http://cran.us.r-project.org/ .

Other Sources: Beyond the required text, additional material will be drawn from a number of sources. Some additional useful references are:

• Bowman, A.W. and Azzalini, A., (1997), Applied Smoothing Techniques for Data Analysis: The Kernel Approach with S-Plus Illustrations, Oxford Science Publications.
• Efromovich, S., (1999), Nonparametric Curve Estimation, Springer-Verlag.
• Eubank, R.L., (1988), Spline Smoothing and Nonparametric Regression, Marcel Dekker.
• Green, P.J. and Silverman, B.W., (1994), Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach, Chapman and Hall.
• Härdle, W. (1990) Applied Nonparametric Regression, Cambridge University Press.
• Härdle, W. (1991) Smoothing Techniques with Implementation in S, Springer-Verlag.
• Hart, J.D. (1997) Nonparametric Smoothing and Lack-of-Fit Tests, Springer-Verlag.
• Loader, C. (1999) Local Regression and Likelihood, Springer-Verlag.
• Ogden, R.T., (1997), Essential Wavelets for Statistical Applications and Data Analysis, Birkhäuser.
• Schimek, M.G. (ed.), (2000), Smoothing and Regression, Wiley.
• Scott, D.W., (1992), Multivariate Density Estimation: Theory, Practice, and Visualization, Wiley.
• Silverman, B.W., (1986), Density Estimation for Statistics and Data Analysis, Chapman and Hall.
• Thompson, J.R. and Tapia, R.A., (1990), Nonparametric Function Estimation, Modeling, and Simulation, SIAM.
• Wand, M.P. and Jones, M.C., (1995), Kernel Smoothing, Chapman and Hall.

Disability Statement: If a student has a disability that will likely require some accomodation by the instructor, the student must contact the instructor and document the disability through the Disability Resource Center, preferably during the first week of the course. Any requests for special considerations relating to attendance, pedagogy, taking of examinations, etc. must be discussed with and approved by the instructor. In cooperation with the Disability Resource Center, course materials can be provided in alternative formats - large print, audio, diskette or Braille.

Disclaimer: The instructor reserves the right to alter anything about this course, pretty much on whim (but he probably won't).