STAT 592B: Special Topics: Semiparametric Models

Winter Quarter 1998

Announcement

Basic Information:

• Professor: Jon A. Wellner
• Times: T - Th, 10:30 - 12:00
• Place: C301, Padelford Hall
• Credits: 3
• Prerequisites: Statistics 583
• Recommended Text:
  Efficient and Adaptive Estimation for Semiparametric Models,
  by P.J. Bickel, C.A.J. Klaassen, Y. Ritov, and J.A. Wellner,
  Johns Hopkins University Press, Baltimore.
  

This course will begin with a review of information lower bounds for estimation in parametric, nonparametric, and semiparametric models. The geometric features of tangent spaces will be used as a unifying theme. Lower bounds in the form of Hajek - LeCam type convolution theorems will be given for estimation of both Euclidean (finite - dimensional) and general (infinite - dimensional) parameters. Recent results characterizing differentiable and regularly estimable functions in semiparametric models will be presented. Examples will be drawn from: group models, regression models, transformation models, censoring and missing data models, and mixture models.

After reviewing information bounds, the main emphasis of the course will be on construction of efficient estimators; i.e. estimators which achieve the information bounds. We will review recent research in this direction by Van der Vaart, Van der Vaart and Murphy, Huang, and others.

Topics / Outline:

I. Information Lower Bounds for Semiparametric Models

1. Contiguity theory; the Hajek - LeCam convolution theorem for parametric models
2. Convolution theorems for Euclidean parameters in nonparametric and semiparametric models
3. Examples for Euclidean parameters
4. Convolution theorems for general parameters:
   • Characterization of differentiable functionals
   • Characterization of regularly estimable parameters

II. Construction of Estimators:

1. Construction of efficient estimators: basic results.
2. General M - estimation results and techniques: van der Vaart's theorem.
3. Maximum - likelihood estimates in "smooth" semiparametric models: Huang's theorem and applications.
4. Attainment of information bounds more generally: Bickel and Ritov; Birge and Massart.

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

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