Higher order Influence Functions and Minimax Estimation of Nonlinear Functionals

Nov 1 (Tuesday) at Noon GHC-8102

Speaker: James Robins, Havard School of Public Health

Abstract: I present a theory of point and interval estimation for nonlinear functionals in parametric, semi-, and non-parametric models based on higher order influence functions. The theory reproduces many previous results, produces new non-root n results, and opens up the ability to perform optimal non-root n inference in complex high dimensional models. We present novel rate-optimal point and intervals estimators for various functionals of central importance to statistics and biostatistics in settings in which estimation at the expected root n rate is not possible, owing to the curse of dimensionality.