STAT 593D:

Empirical Processes: Theory and Applications

Spring Quarter 2003

Syllabus (last updated: 3/13/2003)

Course personnel:

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

Administrative Information:

• First Meeting: Thursday, April 3.
• Tentative Meeting Times: T-Th 10:30 - 12:00
  
• Place: Padelford Hall C301

Prerequisites:

• Successful completion of STAT 582
• STAT 521 or equivalent
• Interest in empirical processes

Required Texts:

• A. W. Van der Vaart and J. A. Wellner, Weak Convergence and Empirical Processes, Springer-Verlag, 1996.

Supplemental Texts:

• Van de Geer, S. A. (2000). Empirical Processes in M-Estimation. Cambridge University Press.
• Ledoux, M and Talagrand, M. (1991). Probability in Banach Spaces. Springer-Verlag, New York.
• Pollard, David. (1990). Empirical Processes: Theory and Applications. NSF - CBMS Regional Conference Series in Probability and Statistics, Volume 2, IMS, Hayward, American Statistical Association, Alexandria.
• Dudley, R. M. (1999). Uniform Central Limit Theorems. Cambridge University Press.

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:

• Homework: 70%
• Participation: 30%

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.

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