Higher-Order Influence Functions and Minimax Estimation of Nonlinear Functionals

• Activity Number: 600
• Type: Invited
• Date/Time: Thursday, August 5, 2010 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): James Robins*+
• Companies: Harvard School of Public Health
• Keywords: higher order ; influence function ; minimax estimation

Abstract

I describe recent advances in the theory of estimation with higher order influence functions. The thoery is a theory of point and interval estimation for nonlinear functionals in parametric, semi-, and non-parametric models that applies equally to both vn and non-vn problems . The theory reproduces results previously obtained by the modern theory of non-parametric inference, produces many new non-vn results, and most importantly opens up the ability to perform non-vn inference in complex high dimensional models, such as models for the estimation of the causal effect of time varying treatments in the presence of time varying confounding and informative censoring. Higher order influence functions are higher order U-statistics. The theory extends first order semiparametric theory based on first order influence functions.