STAT 592:
Empirical Processes

Winter Quarter 1999

Syllabus (last updated: 1/3/99)

Course personnel:

• Professor: Jon A. Wellner
• B320 Padelford Hall
• Phone: 543-6207
• Office hours: 1:30 - 3:30 MWF; or by appointment

Administrative Information:

• Time(s): MWF 9:30 - 10:20
  
• Place: MW Padelford C-301; F Music ?? .

Prerequisites:

• Successful completion of STAT 583
• STAT 521-2-3 would be helpful
• Interest in empirical processes

Required Texts:

• A. W. Van der Vaart and J. A. Wellner, Weak Convergence and Empirical Processes, Springer-Verlag, 1996.
• Sara A. Van de Geer, Applications of Empirical Process Theory, Cambridge University Press, 1999. (to be handed out as the quarter progresses).

Supplemental Texts:

• M. Ledoux and M. Talagrand, Probability in Banach Spaces, Springer-Verlag, New York, 1991.
• David Pollard, Empirical Processes: Theory and Applications. NSF - CBMS Regional Conference Series in Probability and Statistics, Volume 2, IMS, Hayward, American Statistical Association, Alexandria, 1990.

Other Books and Longer Papers:

• Shorack, G. R. and Wellner, J. A. (1986). Empirical Processes with Applications to Statistics, Wiley, New York.
• Pollard, D. (1984). Convergence of Stochastic Processes. Springer-Verlag, New York.
• Dudley, R. M. (1984). A course on empirical processes; Ecole d'Ete de Probabilites de St. Flour. Lecture Notes in Math. 1097, 2 - 142. Springer Verlag, New York.
• Gine, E. and Zinn, J. (1986). Lectures on the central limit theorem for empirical processes. Lect. Notes in Math. 1221, 50 - 113. Springer-Verlag, Berlin.
• Adler, Robert (1990). An Introduction to Continuity Extrema, and Related Topics for General Gaussian Processes. Institute of Mathematical Statistics Lecture Notes - Monograph Series, Volume 12. Institute of Mathematical Statistics, Hayward.

Grading:

• Project: 60%
• Homework: 40%

Tentative Topics / Outline

• Empirical Process Basics:
  Exponential bounds and Chaining;
  Empirical Processes and Gaussian Limits;
  Vapnik - Chervonenkis classes of sets and functions;
  Uniform covering numbers; bracketing covering numbers;
  Glivenko-Cantelli classes; Donsker classes;
• Applications of Empirical Processes to Statistics:
  Likelihood estimation in semiparametric models;
  nonparametric maximum likelihood; regression.
• Adaptive Nonparametric Estimation: isoperimentric inequalities and model selection
  isoperimetric inequalities;
  model selection.

Click here to return to the Statistics Dept. home page.

Click here to return to the University of Washington home page.