This special topics course will treat modern empirical process theory and applications of this theory to a variety of statistical problems. Applications will be drawn from survival analysis, econometrics, semiparametric models, regression and density function estimation, clustering, and classification. I plan to draw on S. van de Geer's new book for many of the applicatons. During the last three-four weeks of the quarter I will cover some of the new isoperimetric inequalities and applications of these inequalities to problems in model selection and adaptive nonparametric estimation.

• 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.

Books:

• Van der Vaart, A. W. and Wellner, Jon A. (1996). Weak Convergence and Empirical Processes, Springer, New York.
• Van de Geer, S. A. (1999). Applications of Empirical Process Theory Cambridge University Press, Cambridge.