JSM 2005 Online Program

Abstract #304667

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Activity Number:	516
Type:	Contributed
Date/Time:	Thursday, August 11, 2005 : 10:30 AM to 12:20 PM
Sponsor:	General Methodology
Abstract - #304667
Title:	Higher Order Influence Functions of Robust Inference in Coarsened at-Random Data Models
Author(s):	Eric Tchetgen*+
Companies:	Harvard University
Address:	13 Ellery St, Cambridge, MA, 02138, United States
Keywords:	Missing data ; curse of dimensionality ; higher order influence functions ; double robustness ; semiparametric ; Coarsening at Random
Abstract:	Suppose we wish to estimate a full data functional b(L) of full data L, based on observed data O that are coarsened at random (CAR). Recent advances in semiparametric theory for CAR models have led to doubly-robust (DR) estimators that are root-n consistent (the standard parametric rate) if either (but not necessarily both) (i) a working model for the missingness mechanism or (ii) a working model for the full data distribution are correctly specified. However, DR estimators are inconsistent if, as is inevitable in high-dimensional data, both working models are misspecified. We introduce novel estimators for the full data functional based on higher-order influence functions of the observed data. These estimators will be consistent for the full data functional of interest under weaker assumptions for (i) and (ii) than required by DR estimators; however, we must sacrifice root-n consistency for slower convergence rates comparable to those encountered in nonparametric inference. We present simulation results demonstrating the performance of our method.

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